The conformity bias exhibited by large language models (LLMs) can pose a significant challenge to decision-making in LLM-based multi-agent systems (LLM-MAS). While many prior studies have treated "conformity" simply as a matter of opinion change, this study introduces the social psychological distinction between informational conformity and normative conformity in order to understand LLM conformity at the mechanism level. Specifically, we design new tasks to distinguish between informational conformity, in which participants in a discussion are motivated to make accurate judgments, and normative conformity, in which participants are motivated to avoid conflict or gain acceptance within a group. We then conduct experiments based on these task settings. The experimental results show that, among the six LLMs evaluated, up to five exhibited tendencies toward not only informational conformity but also normative conformity. Furthermore, intriguingly, we demonstrate that by manipulating subtle aspects of the social context, it may be possible to control the target toward which a particular LLM directs its normative conformity. These findings suggest that decision-making in LLM-MAS may be vulnerable to manipulation by a small number of malicious users. In addition, through analysis of internal vectors associated with informational and normative conformity, we suggest that although both behaviors appear externally as the same form of "conformity," they may in fact be driven by distinct internal mechanisms. Taken together, these results may serve as an initial milestone toward understanding how "norms" are implemented in LLMs and how they influence group dynamics.