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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 direct reply. Second, we examine whether the toxicity of the first direct reply to a toxic tweet in conversations establishes the group norms for subsequent replies. By doing so, we outline how bystanders and the tone of initial responses to a toxic reply are explanatory factors which 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 156k tweets belonging to ~9k conversations. Central to this work is the social psychological research on the "bystander effect" documenting that the presence of bystanders has the power to alter the dynamics of a social situation. If the first direct reply reaffirms the divisive tone, other replies may follow suit. We find evidence of a bystander effect, with our results showing that an increased number of users participating in the conversation before receiving a toxic tweet is negatively associated with the number of Twitter users who responded to the toxic reply in a non-toxic way. We also find that the initial responses to toxic tweets within conversations is of great importance. Posting a toxic reply immediately after a toxic comment is negatively associated with users posting non-toxic replies and Twitter conversations becoming increasingly toxic.