Social animals interact frequently with conspecifics, and their behaviour is influenced by social context, environmental cues and the behaviours of interaction partners, allowing for adaptive, flexible adjustments to social encounters. This flexibility can be limited by part of the behavioural variation being genetically determined. Furthermore, behaviours can be genetically correlated, potentially constraining independent evolution. Understanding social behaviour thus requires carefully disentangling genetic, environmental, maternal and social sources of variations as well as the correlation structure between behaviours. Here, we assessed heritability, maternal, common environment and social effects of eight social behaviours in Neolamprologus pulcher, a cooperatively breeding cichlid. We bred wild‐caught fish in a paternal half‐sibling design and scored ability to defend a resource against conspecifics, to integrate into a group and the propensity to help defending the group territory (“helping behaviour”). We assessed genetic, social and phenotypic correlations within clusters of behaviours predicted to be functionally related, namely “competition,” “aggression,” “aggression‐sociability,” “integration” and “integration‐help.” Helping behaviour and two affiliative behaviours were heritable, whereas there was little evidence for a genetic basis in all other traits. Phenotypic social effects explained part of the variation in a sociable and a submissive behaviour, but there were no maternal or common environment effects. Genetic and phenotypic correlation within clusters was mostly positive. A group's social environment influenced covariances of social behaviours. Genetic correlations were similar in magnitude but usually exceeding the phenotypic ones, indicating that conclusions about the evolution of social behaviours in this species could be provisionally drawn from phenotypic data in cases where data for genetic analyses are unobtainable.