Disunion describes what happens when a club disbands or a marriage breaks up. The disunion of your book group means all the members have gone their separate ways.
The noun disunion means the coming apart of some connection or alliance, and because it's such a formal word it's often used to talk about governments or business federations. You could say that the disunion of Britain and India resulted in Partition, or that the US Civil War nearly ended in disunion. The word combines dis, "lack or not," and union, with its Latin root of unionem, "oneness or unity."