The National Football Conference is the half of the NFL that was originally the teams in the NFL at the time of the merger with the AFL, save the franchises in Cleveland, Baltimore and Pittsburgh at the time that volunteered to play with the former AFL teams to balance the amount of teams in each conference. The Conference is split into four 4-team Divisions and they play ultimately for the NFC Championship, in order to represent the NFC in the Super Bowl.
Here is a team by team look at the NFC
