A Renegade Dalek attacks its prey
The Renegade Daleks were a faction of Daleks loyal to the Supreme Dalek and against Davros, because he wanted to change the way Daleks were created and how they operated. The Renegades saw Davros's experiments with grafting mechanics to Dalek flesh as heresy, and the Dalek Civil War broke out after Davros became Emperor of the Daleks.
The Renegades fought agaisnt Davros's Imperial Daleks for thousands of years and across many planets, and neither side could secure victories for long. The Renegades had to abandon the Dalek homeworld of Skaro at the very beginning of the War, but the Imperial forces did not settle there until later. However, the Renegades defeated the Imperials by destroying their base planet of Necros.
The 'Supreme' Dalek
The Renegades main base of operations was on the planet Antalin, but near the end of the war the Imperials discovered it and sent the majority of their fleet to destroy it. The Supreme Dalek fled to Earth with a taskforce of Renegade Daleks to recover the ancient Time Lord weapon known as the Hand of Omega, which he knew would win the war for the Renegades if it was correctly used.
During this mission, the Renegade stronghold at Antalin fell, and the surviving Renegade Daleks were rounded up. Many were simply killed, but some of the higher ranking ones were taken to Davros, who eventually learned of the Renegade Dalek's mission to Earth. Aware that there was a small taskforce nearby, Davros sent them to intercept the Supreme Dalek.
Renegade Daleks used efficient ground tactics to annihilate the Imperials
However, the Supreme Dalek and his forces destroyed the Imperial taskforce and landed on Earth. Enraged, Davros personally oversaw the mission and flew the Dalek Mothership to the area the Renegades had landed. However, Renegade Daleks attacked the Dalek Mothership and they were forced to retreat. Instead, Taskforces were sent down to recover the Hand.
Outnumbered and Outgunned, the Supreme Dalek was running out of options. But then he realised that the Hand was active - The Doctor had reprogrammed it. He allowed the Imperials to break into the Renegade base to capture the Hand, and he escaped the battle alone. The Hand of Omega was used by Davros and, due to the Doctor's tampering, it destroyed the Dalek homeworld of Skaro and annihilated the Imperial Daleks there. The remaining Renegades engaged the remaining Imperials in a massive battle above Earth, but the Hand flew back and annihilated them as well, negating both teams and ending the Dalek Civil War.
The Supreme Dalek later self-destructed out of shame and fear, since he was the last of his kind on Earth and there was no home for him to go to, and no way for him to get there.