Faction

A faction (a political group) is a group of people who want to run the government's policies in THEIR best interests.

[I find the above POV and inaccurate. I don't have a good definition on tap though.]

They have different policies and appeal to voters (in countries with voting) for their votes, or; in counrties without votes, appeal to them directly to overthrow the existing government by force. Examples of easily recognized factions are: Democrats, Republicans, and the Green Party.