What conference has won the most collegiate national football championships?

Ohio State is one of only two universities (the University of Michigan being the other) to have won an NCAA national championship in baseball, basketball and football. Ohio State has also won national championships in men's swimming & diving, men's outdoor track & field, men's golf, men's gymnastics, men's fencing, co-ed fencing, and synchronized swimming. Since the inception of the Athletic Director's Cup, Ohio State has finished in the top 25 each year, including top 6 finishes in three of the last five years. During the 2005-2006 school year Ohio State became this first Big Ten team to win conference championships in football, men's basketball and women's basketball in the same season.