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)

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)

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)