Social group structure is highly variable and can be important for nearly every aspect of behavior and its fitness consequences. Group structure can be modeled using social network analysis, but we know little about the evolutionary factors shaping and maintaining variation in how individuals are embedded within their networks (i.e., network position). While network position is a pervasive target of selection, it remains unclear whether network position is heritable and can respond to selection. Furthermore, it is unclear how environmental factors interact with genotypic effects on network positions, or how environmental factors shape selection on heritable network structure. Here we show multiple measures of social network position are heritable, using replicate genotypes and replicate social groups of Drosophila melanogaster flies. Our results indicate genotypic differences in network position are largely robust to changes in the environment flies experience, though some measures of network position do vary across environments. We also show selection on multiple network position metrics depends on the environmental context they are expressed in, laying the groundwork for better understanding how spatio-temporal variation in selection contributes to the evolution of variable social group structure.