Dalek splinter group

As recorded in the Dalek Combat Training Manual the Time Lords made reference to Dalek splinter groups which deviated from conventional Dalek mentality, purity and authority. (PROSE: Dalek Combat Training Manual)

Factions

The Time Lords believed the first instance of a Dalek splinter group (PROSE: Dalek Combat Training Manual) to be the Humanised Dalek, originally test Daleks who were implanted with the Human Factor as part of the Dalek Emperor's Operation Human Factor. Though this was intended by the Emperor to isolate the Dalek Factor and implant it in humans, the Second Doctor saw that many Humanised Daleks were created. These Daleks went on to question their orders, leading to a Dalek Civil War within the Dalek City on Skaro. (TV: The Evil of the Daleks)

Challenging the authority of the Supreme Dalek, Davros, the Daleks' creator, used an indoctrination serum hypodermic to condition a number of Daleks and Dalek duplicates to serve him. Though they were killed in battle against the Daleks in the Duplicate Incident, (TV: Resurrection of the Daleks) Davros himself escaped to Necros, where he created a new race of Daleks from the Resting Ones on Tranquil Repose. Having been alerted by Lancelot Takis, Daleks from Skaro came to Necros and fought through first of these Daleks whilst Orcini set off an explosion in Davros' bunker, killing many of Davros's prototypes. Davros was then apprehended by the Daleks, who intended to take Davros to Skaro for trial whilst the surviving Necros Daleks were to be reconditioned to obey the Supreme Dalek. (TV: Revelation of the Daleks)

Eventually, Davros succeeded in usurping the rule of the Dalek Emperor and "Imperial Daleks" on Skaro. (COMIC: Emperor of the Daleks!) As he took the position of Emperor Dalek, Davros's new army of Daleks became Imperial Daleks and engaged in a war with the now Renegade Daleks following the Supreme Dalek. As Davros had modified his Dalek mutants, they conflicted with the purity of the Renegade Daleks. (TV: Remembrance of the Daleks)

Devised by pacifist scientist Gonzo Orcini as a "refined, highly intellectual version" of the "old Daleks" created by Davros, the Orcini New Daleks initially followed his ideals but ultimately fell in with conventional Dalek mentality. (PROSE: War and Peace)

Created by Professor Martez on Red Rocket Rising, the Mutant Daleks welcomed the Daleks of Skaro to their planet, as they had been summoned by Martez to assist in their development. The Skaro Daleks, however, identified them as a "deviation from the purity of the Dalek bloodline" and so saw to their extermination. (AUDIO: Blood of the Daleks)

Individual cases

Having come into contact with Rose Tyler's human DNA, the Metaltron, which was at the time believed to be the last Dalek in existence, found that it was mutating and developing emotions. Deeming this an unacceptable outcome, the Dalek initiated self-destruct. (TV: Dalek)

Designated as a traitor, one bronze Dalek came to believe that the Daleks should be destroyed since while they were originally created to ensure the survival of the Kaleds, their mission had deviated and eroded Kaled identity. Upon hearing this, the Thirteenth Doctor remarked that Davros would be both impressed and horrified. Though offering to assist the Doctor in destroying the Daleks, this Dalek was itself intercepted and exterminated. (TV: The Power of the Doctor)