Social networks influence important aspects of our daily lives. Many of our behaviors and opinions originate from contact with our peers, friends, co-workers, and others who comprise our social networks. Although social scientists have primarily studied how one person's behavior can influence another person's behavior, much of the social influence we experience comes from groups of people rather than singular individuals. Nevertheless, how we respond to group influence is poorly understood in social science research. Here we show that disconnectedness among our peers leads us to adopt their low-cost and low-engagement behaviors while connectedness among our peers leads us to adopt their high-cost and high-engagement behaviors. This resolves an important debate in social science research, which has produced contradictory results that support both connectedness and disconnectedness among one's peers as sources of group influence. Broadly, our results suggest that the diffusion of different phenomena, such as social protest or clothing fashions, require different social network structures. Moreover, we predict that highly interconnected social networks facilitate the spread of high-engagement behaviors such as political participation, while sparsely connected networks facilitate the viral adoption of consumer products, media, and fashion.