In group-living species, natural selection should favor behavioral strategies that collectively give rise to structures that facilitate group persistence and minimize conflict among group members. However, the extent to which conflict is present in a group, as well as how conflict is resolved, varies widely among groups; some groups have relatively little conflict while others disband due to high levels of conflict. Here, we seek to understand how both within-group and between-group changes alter group stability and social network structure in the group-living cichlid, Neolamprologus pulcher. We find that network changes can be related to both within-group and between-group differences in social structure. First, we demonstrate that there are unique characteristics of groups that remain intact compared to those that disband. Second, we demonstrate that group characteristics and the presence of neighbors alter the target of conflict within the group, shifting how aggressive, submissive, and affiliative interactions are divided among individuals of different sizes and dominance statuses. Collectively, our results demonstrate that both within and between group social structure should play a key role in predicting conflict within groups and group persistence.