Online harassment and abusive language continue to be a growing concern on social media platforms. In this study, we explore the power of group dynamics to shape the toxicity of Twitter conversations. First, we examine how the presence of others in a conversation can potentially diffuse Twitter users' responsibility to address a toxic reply. Second, we examine whether the toxicity of the first direct reply to a toxic tweet in conversations establishes group norms for subsequent replies. By doing so, we outline users participating in the conversation before the first toxic reply and the tone of initial responses to a toxic reply as explanatory factors that affect whether others feel uninhibited to post their own abusive or derogatory replies. We test this premise by analyzing a random sample of more than 187K tweets belonging to ~ 9K conversations. This analysis of group dynamics is motivated by a larger body of scholarship on contagion of antisocial behavior and the power of establishing social norms that maintain rather than sanction toxicity. We find evidence that an increased number of users participating in the conversation before receiving a toxic tweet is negatively associated with the number of users who responded to the toxic reply in a non-toxic way. Furthermore, posting a toxic reply immediately after a toxic comment is negatively associated with users posting non-toxic replies and Twitter conversations becoming increasingly toxic. We argue that understanding how social media users respond to uncivil comments or abusive language reveals social norms as powerful social cues that can shape human behavior online.