I didn’t know mafia was this complicated
The basic idea of Mafia is that out of all the people playing, there's a small group of betrayers trying to bring everyone else down. The betrayers are the Mafia, sometimes called "scum" or other unpleasant names. Everyone else is in the Town, otherwise called "villagers" or "innocents" or so forth.
The Town's goal is to get rid of all the scum players. They do this by taking a majority vote each game Day for who they want to get rid of. The Mafia's goal is to outlast all of the Townies until they control the majority vote, at which time there's nothing the Town can do to stop the scum from completely taking over. They can do this by avoiding being voted out and killing players during the Night phases following each game Day. The crowd that starts the game gets whittled down until eventually only one faction remains in the game.
The cycle of Day and Night continues until either all of the Mafia have been removed from the game or all of the Townies have been removed from the game.
Also, if there is 3rd party then it also considers a faction in its own
Example cult that we have in this game, I suppose:
A Cult is a third-party group that seeks to recruit players into itself. The recruitment is done by a Cult Leader who is typically the only member of the Cult at the beginning of the game.