break up means start laughing or stop classes and start the holidays (e.g. The kids just broke up as soon as they saw a comedian. The School broke up for the summer holidays in Jun.)
break up of means divide into smaller groups (e.g. It will make our power weaker if we break up of team work.)
break up with somebody means separate (= split up) (e.g. I’m surprised to hear that Tom have broken up with Marry.)

more about the Phrasal Verbs …