Many social animals live in stable groups. In contrast, African savannah elephants (Loxodonta africana) live in unusually fluid, fission–fusion societies. That is, ‘core’ social groups are composed of predictable sets of individuals; however, over the course of hours or days, these groups may temporarily divide and reunite, or they may fuse with other social groups to form much larger social units. Here, we test the hypothesis that genetic relatedness predicts patterns of group fission and fusion among wild, female African elephants. Our study of a single Kenyan population spans 236 individuals in 45 core social groups, genotyped at 11 microsatellite and one mitochondrial DNA (mtDNA) locus. We found that genetic relatedness predicted group fission; adult females remained with their first order maternal relatives when core groups fissioned temporarily. Relatedness also predicted temporary fusion between social groups; core groups were more likely to fuse with each other when the oldest females in each group were genetic relatives. Groups that shared mtDNA haplotypes were also significantly more likely to fuse than groups that did not share mtDNA. Our results suggest that associations between core social groups persist for decades after the original maternal kin have died. We discuss these results in the context of kin selection and its possible role in the evolution of elephant sociality.