 What are social groups? One debate in the literature concerns the kind of entities that social groups are: collections, classes, sets, fusions, structures, or some other kind of entity. It may seem natural to think of a group as a set of people in the mathematical sense. However, groups can persist through changes in membership, while sets are generally understood as having their members essentially (see Sharvy 1968, Ruben 1985, Uzquiano 2004, Sheehy 2006). Effingham (2010) proposes an account that identifies groups with complex sets, so that they can have different members at different times and at different worlds. Others (including Macdonald &amp; Pettit 1981, Copp 1984, Sheehy 2006) argue that groups are fusions of people. A problem with this is the transitivity of parthood: since Alice’s finger is a part of Alice, it follows from the fusion view that if Alice is a part of a group, then so is Alice’s finger. That is a problem, because while Alice is a member of the group her finger is not. Another view is that groups are realizations of structures: Schmitt (2003a) considers and objects to this, and Ritchie (2013) defends it. Others argue that groups are distinct from their members but are constituted by them (Uzquiano 2004, Jansen 2009, Epstein 2015).