In many social animals, groups recurrently split into subgroups that regularly re-merge. Such fission-fusion behavior allows individuals to better balance the cost and benefits of group living. However, maintaining a large number of close social links in groups with fission-fusion dynamics may be difficult. It has been suggested that this is the reason why in several species, large groups show more subunits (higher modularity) than do small ones. Many bat species exhibit fission-fusion dynamics in their colonies. This makes them well suited to investigate the proposed link between group size, stability of social links, and group modularity. We studied the daily roosting associations of a Natterer’s bat colony (Myotis nattereri), where up to 80 members carried individual RFID-tags. Based on more than 10,000 individual recordings, we analyzed the influence of relatedness, age, sex, and breeding status on the colony’s social network structure during three breeding seasons. We found an almost fully connected social network with very low modularity and generally weak pairwise associations. Nevertheless, the relative strengths of associations between individuals remained stable across years. Sex, age, and breeding status significantly influenced the strength of an individual’s associations and determined the influence of individuals in the network. In general, associations between bats that were similar in all abovementioned traits were stronger than those between dissimilar individuals. Our results show that despite high fission-fusion dynamics, large colony sizes, and low modularity of their social network, Natterer’s bats were able to maintain stable long-term associations. For a variety of social and ecological reasons, large social groups often consist of several communities with stronger individual bonds within and weaker individual bonds between such social subunits. Unlike that predicted for its relatively large size, the studied Natterer’s bat colony that consisted of up to 80 individually marked bats was not subdivided into communities. Despite the fully connected network, the individual associations were not random. Instead, their strength was mainly driven by relatedness and similarity in age and breeding status of the colony members. Moreover, we found stable long-term pairwise relationships between individuals across several years. Our study shows that despite the strong fission-fusion behavior and large size of their colony, Natterer’s bats formed a fully connected, unimodal social network.