Basically, a group who separates from a larger organization - holding the main beliefs or goals of the original, but are wholly or mostly evil.
Two common ways of applying this trope:
The writer doesn't want to paint some organization, nation or religion black. It may be a real-world institution, or an institution from this fictional world which was previously described as at least semi-decent. But the author still wants villains belonging to it, so they invent a renegade group.
A faction that operates without authorization, and their methodology differs from the main body. Often they are extremists: escalating a conflict, willing to break the rules, far more infamous than their mother alignment - but this isn't always the case.
Note that it doesn't apply to out and out turncoats: the faction must still keep the general ideas of the original; only with less benevolent policies. If the factions are religious in nature, related to The Heretic. Can result in Enemy Civil War. Renegade Russian is a common nation-specific subtrope, since Russians and Soviets get this treatment especially often. If the original organization was bad-ish, but not bad enough, this may result in The Good, the Bad, and the Evil. This may be used to provide an inversion of My Species Doth Protest Too Much by setting up an antagonist, then revealing that the rest of their faction doesn't like them either.
For the individual version, see Rogue Agent.
Blue Cosmos, an anti-Coordinator terrorist group and movement within the Earth Alliance. Many in the Alliance don't share such extremist views. Sadly, Blue Cosmos ends up gaining enough influence to control the policies of the government.
The Clyne Faction. Originally the Moderates within ZAFT, they broke off when the Zala extremists came to power. Subverting the trope, they're outright good guys. The Faction managed to form a underground resistance, steal key equipment, and join up with the heroes.
The Treize Faction in Gundam Wing. A splinter group of OZ / the Romafeller Foundation, the Faction opposed the introduction of automated mecha. An inverse of the trope, the splintering had made Foundation come off as increasingly villainous.
In Mobile Suit Gundam Wing Endless Waltz, it's revealed that the Gundam pilots had split from the Barton Foundation. Disagreeing over the goal of world conquest, the pilots decide to focus on stopping OZ instead.
La Eden, a violent right-wing political group within the AEU, though not supported by the Superpower. The group commits a series of terror attacks to stop the protagonists. Celestial being responds by simultaneously curbstomping the entire faction.
Team Trinity claims to be part of Celestial Being, sharing the similar technology and goal of eliminating warfare. However, the Trinities are much more ruthless - attacking without provocation nor mercy. Eventually, the two groups come into conflict.
The Innovators were originally part of Celestial Being. But thanks to the events of Season 1, the two groups splinter, with the Innovators causing most of the problems for the next season.
The ESF Coup detat Faction. Splintering off from the Federation military, the Coup seeks to expose the A-Laws' atrocities. Like the Trieze Faction, their going "renegade" makes the Earth Sphere Federation come off as increasingly antagonistic.
The Titans in Mobile Suit Zeta Gundam. Though officially part of the Earth Federation serving as a special security force, the group was used by a corrupt politician to gain control of the Earth Sphere. Their actions were zealous, which including gassing an entire colony. Eventually they went full renegade after they were exposed by the AEUG.
The sinister Beylin Fist faction in Metal Fight Beyblade. The group had splintered from China's Beylin Temple training school.
In Digimon Tamers, the protagonists thought that since the Devas were serving one Digimon Sovereign, then all four might be against them. It turns out Zhuqiaomon, the Sovereign who the Devas serve, is acting on his own. He and the other three leading Digimon couldn't agree on a single defense strategy against the D-Reaper.
WILLE of Rebuild of Evangelion, consisting of former NERV agents who oppose the progenitor agency. An inversion of the trope, WILLE goals are benevolent compared to NERV.
Nextwave split itself off from H.A.T.E. when they learned that HATE was actually owned by the Beyond Corporation, which was a cover group for S.I.L.E.N.T., their ostensible nemesis. Nextwave tries to do good when they're not on the run from their employers.
The Sand Blast City Freedom Fighters in Archie Comics' Sonic the Hedgehog. Unlike the other Freedom Fighters, the Sand Blasters are ruthless and their actions questionable. It was because of their abusive treatment that the deroboticized Robians joined the Eggman Empire. Yes, it got so bad that the former slaves entered into an alliance with their former master.
In Marvel Comics, HYDRA has had several splinter groups: AIM, the Hand, and the Secret Empire among others.
The Crimson Jihad in True Lies is a splinter group that broke off of a larger Islamic terrorist organization, apparently because their leader Salim Abu Aziz didn't think the bigger group was crazy enough.
General Chan Lu from the remarkably silly Battle Beneath The Earth is an example of the Renegade Chinese version.
The crew of the Narada in the 2009 Star Trek. When Captain Pike confronts the Narada, he states that the Federation and the Romulan Star Empire are not at war with each other. However, Nero replies that his crew do not represent the Empire, as they "stand apart". Which is the truth: in Nero's time, there isn't much left of the Romulan Star Empire, as Romulus and Remus were wiped out by a supernova.
Blown Away takes great pains to emphasize that the villain was definitely not in the IRA, because he was "too crazy for them." (Oddly, the film is less reticent about claiming that he did freelance work for the Red Brigades and the Libyan government. Maybe the IRA just had a better P.R. department than they did?)
It may go full rogue, but the ending implies that they still continue following their original mandate, as the news report mentions the destruction of a yacht belonging to a sheik suspected of funding terrorists.
Fëanor and his sons and followers in The Silmarillion are more or less a Renegade Faction of the High Elves.
In the novel Patriot Games and its film adaption, the Ulster Liberation Army is a Marxist splinter faction of the Provisional IRA. Naturally, the ULA is more ruthless than the group they left.
In the Frontier Magic series, the mainstream Rationalists simply believe that not being dependent on magic is a good idea; but an isolated settlement of fanatical Rationalists ends up condemning magic as evil.
The Faithful of the Church of Humanity Unchained, who settled Masada in the Honor Harrington series. Originally part of the Church of Humanity Unchained on the planet Grayson, they broke from the main church over theological disputes. In contrast to the Grayson church, the Masadans are such extremists that they've rejected all of the New Testament.
The Second Imperium, the Imperial faction from the Star Wars: Young Jedi Knights book series, was retconned to be one of these because another series, Hand of Thrawn, established that a peace treaty was brokered a few years earlier between the Republic and the mainstream Imperial Remnant under the leadership of the relatively nice mustachioed Admiral Gilad Pellaeon.
At least two post-Deep Space Nine continuities (Star Trek Online and Star Trek: Deep Space Nine Relaunch) features renegade Dominion forces in the Alpha Quadrant that refuse to acknowledge that the Dominion War is over (several, in the case of Online, who in addition to featuring three groups allied under a single banner — rogue Alpha Jem'Hadar, the Cardassian True Way, and Laas' New Link — has a time-shifted Dominion fleet refuse to give up their occupation of Deep Space Nine even after being informed by Dominion officials that the war is over).
Another Star Trek example is the Maquis. A paramilitary group that oppose the Cardassians. Originally consisting former Federation citizens, the group also had Starfleet officers aiding them illegally. The Dominion wiped them all out after allying with the Cardassians.
The rogue NID of Stargate SG-1 was this for Earth. While the regular NID was rather shady, the renegade group turned outright criminal, stealing technologies the SGC had failed to negotiate for from other planets, including from Earth's allies the Tollans and the Asgard. Eventually, the rogue NID finally splintered off into The Trust once their wealthy backers were arrested. Freed from any government restrictions, The Trust was even more violent - conducting chemical attacks and assassination. When their operatives were driven away from Earth by the SGC, the group managed to get themselves captured and implanted with Goa'uld. Ironically, Ba'al and Athena ended up in charge of The Trust, and headed several major corporations.
In one second-season episode the SGC encounters a species of aliens called the Reetou who exist out-of-phase from the rest of the universe (read: they're invisible), and were mostly exterminated by the Goa'uld because proximity gives the snakes headaches. One faction of Reetou decided to exterminate the Goa'uld, and that the best way to do it was a scorched-Earth (pardon the pun) policy against humanity, whom the Goa'uld use as hosts. The Reetou Central Authority found this reprehensible and sent an agent to Earth to warn the SGC.
Good/evil-flipped with the Ancients, a splinter group from their progenitor race the Ori who believe that Sufficiently Advanced Aliens should not play god, whereas the Ori do.
Homeguard in Babylon 5. The group was a xenophobic paramilitary faction within the Earth Alliance, committing attacks on aliens.
The xenophobic Terra Prime, committing terrorist acts so humanity adopts an isolationist stance.
Alias: SD-6 worked as a sometimes-splinter group of the Alliance of Twelve, since its head Arvin Sloane had his own agenda apart from the Alliance.
An episode of NCIS features a group called the "MAH" (Military At Home), who believe that America should focus on fighting crime and social problems, instead of policing the world. A group of MAH decides to take it a step further, plotting to destroy a communications tower to make a point, with no intention of harming anyone. However, the renegade group also had a splinter group who decide to attack people as well.
Andromeda has the Knights of Genetic Purity, who utilize highly-advanced technology to hunt down and eliminate any genetically-engineered humans, particularly Nietzscheans, whom they blame (rightly) for the fall of the Commonwealth. While they're too weak to take on the major Nietzschean prides like the Drago-Kazov and the Sabra-Jaguar, they have no problems with going after the lesser ones. Then it's revealed that the Genites (as they're known) are a splinter group of the Templars, founded by Admiral Constanza Stark, Dylan's former superior. While the Templars mainly focus on secretly helping rebuild the Commonwealth, they also plan to destroy the Nietzscheans. The Genites simply take it one step further and go after all genetically-engineered people (Dylan himself is half-Heavy Worlder). It's also clear that the Genites are much better equipped than their parent organization.
Doctor Who has the, ahem, Renegade and Imperial Daleks in "Remembrance of the Daleks," though the split somewhere around "Destiny of the Daleks." Their struggles concern questions of genetic purity; also, the Imperials were full-on cyborgs of Davros' creation.
The Word of Blake in BattleTech, which broke off from ComStar. When the mother organization reformed to lessen focus on it's mystical aspects, the conservatives broke off. The Word eventually started an all-out war that affected in entire Inner Sphere.
The eponymous Delta Green. Once working for the government, it illegally continues its operations to defend America from the Mythos.
2nd Edition Dungeons & Dragons supplement The Complete Druid's Handbook. The Shadow Circle is a secret society of druids within the larger druidic order. It sees Nature as a hostile, cleansing force that ensures the survival of the fittest and thinks that civilization has weakened humanity and the demihuman races. They support barbarians and think that people should go back to nature. They use evil and vicious tactics to carry out their beliefs.
The Chaos Space Marine Legions split off from the Imperium during the Horus Heresy because Horus was tricked into believing that the Emperor would make himself be worshiped as a God and betray half his Primarchs. The Horus Heresy caused that to happen. And it's heavily implied that the Blood Ravens are a splinter chapter from the Thousand Sons Legion.
The Farsight Enclave broke away from the Tau Empire out of a dislike for the Ethereal caste's control of the Empire. Commander Farsight still agrees in principle with the aims of the Empire; the sticking point is the means.
It may be an Inversion since both the Farsight Enclaves and the Tau Empire have dark secrets.
The Lieutenant of Inishmore: Padraic joined the INLA, a splinter faction of the IRA, after the IRA threw him out for being too psychotic. He is also planning on starting his own splinter group, because he doesn't like that the INLA doesn't stop the drug dealers they "protect" from selling drugs to Catholics. Plentiful lampshades are hung on the "splinter group of a splinter group"-idea.
This basically happened to Team Plasma in Pokémon Black 2 and White 2. N's Plasma just wanted people to stop using pokeballs, though they're still on the 'release your Pokemon' kick. Ghetsis' group wants to take over Unova.
The Brotherhood Outcast faction in Fallout 3 split off from Elder Lyons faction after he decided to actively involve himself in helping the people of the Capital Wasteland. The Outcasts consider themselves the "true Brotherhood" and believe that Lyons and his group have strayed from their original mission.
One mission of Command & Conquer: Generals has a renegade Chinese army (allied with the Middle-Eastern terrorist faction which is the villain of the game) as one of the enemies. In this game, China is one of the "good" factions.
The NSA in Perfect Dark. The director of the agency, Trent Easton, is in league with a shadowy conspiracy. And unlike today's NSA, Easton seems to have his own personal army. In order to accomplish their goals, Easton plans to replace the President with a clone as part of a larger scheme.
The human-supremacist terrorist organization Cerberus started out as the black-ops division of the Human Systems Alliance.
Mass Effect 2 reveals that the geth you spent most of the first game fighting are in fact a splinter faction considered heretics by the mainstream geth population, who call themselves the True Geth. The True Geth believe that they and all other creatures should be free to choose their own fates, whereas the heretics serve and obey the Reapers.
Guild Wars 2 has this for every player race: Humans have bandits, rogues, cutthroats, and other violent criminals. Charr have the dogmatic Flame Legion. Asura compete with amoral Mad Scientist types. Sylvari fight the alien Nightmare Court. Nords struggle against the vicious Sons of Svanir.
In the Command & Conquer: Tiberian Series, The Brotherhood of Nod has a chronic issue with these. Various factions of the Brotherhood end up fighting with each other for power; Kane is the only one to really unite them all. Here are a few notable examples:
The Black Hand, led by Anton Slavik. They go renegade when Hassan (Nod's leader and GDI puppet) tries to execute Slavik.
CABAL, after manipulating both sides to accomplish it's goals. It was so much of a threat that both GDI and NOD work together to eliminate it.
The Marcion-led Black Hand, which was but one of the many splinter factions after CABAL's defeat and Slavik's death. Believing the Brotherhood strayed from it's "pure" path, Marcion took the Black Hand into exile, and reformed the group into a religious order.
The Nod Separatists, who opposed Kane's alliance with GDI. They saw it as a betrayal to their own core beliefs.
GDI tends to be a rather stable bunch, but in Tiberian Twilight one GDI army goes rogue over the alliance with Kane, which leads to infighting within the organization.
Skullgirls lore has The Anti-Skullgirl Labs. They conducted research in order to understand the Skull Heart and develop weapons to destroy the Skullgirl it periodically creates. Unfortunately, they weren't exactly known for the humane treatment of their test subjects. After his wife became a Skullgirl and was subsequently killed, the King had a change of heart and decommissioned the Labs, but latter disappeared under mysterious circumstances. Several members of the ASG Labs took advantage of this and moved to restart the experiments, this time without official supervision and with even shadier laboratory practices.
Finally, one sect, Lab Zero, broke off entirely. The members of Lab Zero operate in complete secrecy, even from the other rogue Labs. Their methods are also much, muchmoreheinous than the others.
It's implied that the restarted Labs may have reformed to be more ethical after Princess Parasoul came into power, making the situation an at least partially subverted example of the trope.
After the Covenant disbanded after their defeat in Halo 3, the Elites/Sangheili who disregarded the Arbiter's treaty with humanity broke away to form their own Covenant remnant led by Jul 'Mdama, which are fought in Halo 4. They are unofficially called "the Storm".
The post-3 novels Halo: Glasslands and Halo: The Thursday War shows the Servants of Abiding Truth, one of the precursors to 'Mdama's remnant, fighting a full-on civil war with the Arbiter's faction, one nudged along by the Office of Naval Intelligence to keep them off humanity's back.
In Galactic Civilizations II, mirroring (and probably a deliberate Shout-Out to) the Star Control example, the Korath Clan, which believes that other races should be exterminated outright, rebels against the villainous Drengin Empire.
The Majestic 12 from Deus Ex are that part of the Illuminati who shed "ethical inflexibility".
For a time, The Patriots of Metal Gear Solid series were the American faction of the original Philosophers. The truth is a little more complicated. There was a splintering of the Philosophers when the Wisemen's Committee died off, with the American, Chinese, and Russsian groups breaking off from one another. The conflict in Metal Gear Solid 3: Snake Eater led to the rise of the American branch. However by Metal Gear Solid: Portable Ops, Zero is tired of the Philosopher's bickering. So he steals back the Philosopher's Legacy and reforms the group into The Patriots.
In Fire Emblem: The Sacred Stones, Eirika faces such a faction during her route. The nation of Carcino is divided between the Kilmt faction (which wishes to stay allies with Frelia) and the Pablo faction (which is aligned with Grado). Using unscrupulous means, Pablo takes over the country and attempts to hinder Eirika.
Played straight with the True Way Alliance, a justification for having Cardassian and Jem'Hadar enemies in the game without conflicting with the ending of Deep Space Nine, where the Dominion and Cardassian Union made peace with the Federation, Klingons, and Romulans and the Cardassians acquired a civilian-ruled government. The True Way are terrorists who want to restore the old military regime and resume the Dominion War. See also Live-Action TV above.
Inverted with the Romulan Republic, the faction for Romulan player characters. They broke away from the Romulan Star Empire after the Hobus supernova and Empress Sela and the Tal Shiar seizing control, and are a democratic polity that just wants to rebuild Romulan society in peace.
In Terra the Shadow Cabal started as a personal army for the Sovereign of the Asurian Empire (the founder is his son), but it mutated into a barely controllable paramilitary faction with its hands in everything from slave-raiding to salvage operations.
It's not that uncommon for terrorist groups and guerrillas to split into factions based on political goals, tactics and where they stand on peace talks.