Although researchers recognize the importance of discussing support for math learning within online learning communities, there is a lack of relevant network classifying methods and analyses at the group level to understand the behavioral differences between groups with varying levels of activity, including their mathematical literacies. In this research, we investigated different groups within a large asynchronous online discussion community for middle school students, focusing on their interaction patterns and the quality of their mathematical engagement. First, we employed an extended Surprise detection algorithm that evaluates interaction quality to classify users into core, periphery, and extra-periphery groups. Following this classification, we performed social network analysis to understand the interaction patterns among these groups. For discourse analysis, we used topic modeling methods to analyze the socio-semantic network structure of the discussions. To assess differences in math literacy and discussion success rates among the groups, we applied the Mann-Whitney U test. Findings indicate that each group is more responsive to its members, with the core group demonstrating a balanced response pattern. X-periphery students primarily engage in casual chats and open queries, indicating a more focused participation aimed at immediate learning needs. Notably, the X-periphery group exhibits the highest math literacy and discussion success rates, suggesting that lower activity levels do not hinder communication efficiency. These findings highlight the importance of considering group dynamics and roles in designing online math learning activities to foster effective communication and support, offering practical insights for sustaining online learning communities through tailored discussion activities.