<p>In group-living organisms, we might expect relationships between social position and other behavioural traits such as exploration, such as if certain patterns of social associations encourage exploration or if certain behavioural types both link different groups and are more likely to explore. However, directly testing these ideas is challenging as exploration can be hard to track in the field and is a difficult trait to measure in the laboratory. Furthermore, invertebrate exploration is less commonly quantified as their small size makes them hard to track. Here we quantified social networks in multiple groups of the gregarious cockroach <i>Blaptica dubia</i> in the laboratory and related three measures of social network position (representing overall sociability, connectedness in local cliques, and connectedness to the wider network) to measures of exploration either assayed alone or as part of an aggregation. We found none of the social network measures related to either of the measures of exploration, which were themselves not correlated. We also found that sociability and connectedness to the wider network were positively correlated, suggesting a single axis of variation in centrality within an aggregation. We found no effects of mass or sex, but there were differences between the two blocks our experiments were performed in, suggesting some effect of observer variability. Overall, our results suggest that exploration is not linked to social behaviour in this species, that cockroaches differ in the social behaviour along a syndrome integrating sociability and the tendency to move between aggregations, and that study replication should be encouraged so we can be confident identified trends are robust.</p>