Understanding the features of a population that predict its extinction risk is a vital basic and applied question in ecology. No systematic theoretical exploration has been conducted to understand the drivers of extinction risk in social animals, even though the dynamics of socially structured populations fundamentally differ from the dynamics of populations without social groups. We model the persistence and extinction of social populations using a branching process that tracks the number of social groups to consider how patterns of within-group growth and social group fissions influence extinction risk. We find that social group size, but not total population size, is a key predictor of persistence time. Extinction risk is primarily driven by i) the stable size of social groups, ii) group fission rate, and iii) patterns of within-group density dependence. Populations consisting of larger social groups are far less extinction prone. Higher fission rates reduce extinction risk with logistic growth, but fission rates have a non-monotonic U-shaped effect on extinction risk with an Allee effect. We clarify unique drivers of extinction in social populations and suggest theoretically informed strategies for the conservation and management of social populations.