We examine the effects of social network structure on inequality in a model of referral hiring that focuses on groups rather than individuals. More random social networks yield higher employment rates than less random ones if the population is integrated or job vacancy information flows are random. However less random social networks allow for better containment of job information inside a group in a segregated population with non-random job information flows, resulting in higher employment rates. We report on the robustness of these findings with respect to the size of minority and majority groups and the amount of social segregation.