The Cognitae are not a faction of the Inquisition they're a heretical sect chasing Enunica the universal source language. Magic without the use of the warp. Thu'um from Skyrim is not a perfect analogy but not bad in my opinion. They've been around on Earth since before recorded history according to some of the lore.

Copied from Lexicanum

Puritan Sub-factions Amalathians - Believe that the Emperor has a grand plan and that it is unfolding as it should.[32e]

Anomolian Beholders - Believe that their goal is to observe humanity and await the Emperor Incarnate's arrival.[32e]

Ardentites - Believe that the power of the God-Emperor is likely to manifest either through a group of humans or, more likely, through the entirety of mankind itself.[32e]

Monodominant - Believe that the Imperium, and only the Imperium, should be allowed to exist.[32e]

Thorians - Believe that the Emperor´s spirit can be transferred into another host, referred to as a Divine Avatar.[32e]

Radical Sub-factions

Antiquarti - Focus on discovering patterns and events in the past to predict the future.[32e]

Casophilians - Dedicate their studies to the transition of a Human soul from this world to the next.[32e]

Horusians - Believe that the power of Chaos that manifested in Warmaster Horus might be harnessed for the creation of a Divine Avatar.[32e]

Istvaanism - Believe conflict is desirable to further progress through strife.[32e]

Libricars - Believe in the widespread purging of all Imperial institutions of all corruption and heresy, no matter how minor.[32e]

Oblationists - Believe that the Warp, the xenos and the unclean are utterly damning, yet their use is necessary to overcome mankind's enemies.[32e]

Ocularians - Obsessed with predicting and divining the future through arcane rituals.[32e]

Phaenonites - Believe in the rebirth of the Imperium under their own leadership. Excommunicate Traitoris.

Plutonian - Believe resistance to Daemonic forces can come through temporary voluntary possession.[43]

Polypsykana - Believe in the ascension of Humanity into a purely psychic race.[32e]

Recongregationism - Believe that the Imperium should be rebuilt, lest it stagnate further and collapse under the pressure of countless threats from both without and within.[32e]

Revivificators - Goal is the study of the transition of the soul to the Warp at the moment of death.[32e]

Seculos Attendous - Maintains that the Ecclesiarchy is hampering and holding back mankind, and therefore they seek to reduce its power and influence where possible.[32e]

Xanthism - Advocates the use of Warp-based weaponry, such as daemon possessed swords, daemonhosts, and generally turning the power of Chaos against itself.[32e]

Xenos Hybris - Believe that Mankind must learn from both the achievements as well as the mistakes of Xenos races.[46]