An infodemic is an emerging phenomenon caused by an overabundance of information online. This proliferation of information makes it difficult for the public to distinguish trustworthy news and credible information from untrustworthy sites and non-credible sources. The perils of an infodemic debuted with the outbreak of the COVID-19 pandemic and bots (i.e., automated accounts controlled by a set of algorithms) that are suspected of spreading the infodemic. Although previous research has revealed that bots played a central role in spreading misinformation during major political events, how bots behaved during the infodemic is unclear. In this paper, we examined the roles of bots in the case of the COVID-19 infodemic and the diffusion of non-credible information such as "5G" and "Bill Gates" conspiracy theories and content related to "Trump" and "WHO" by analyzing retweet networks and retweeted items. We show the segregated topology of their retweet networks, which indicates that right-wing self-media accounts and conspiracy theorists may lead to this opinion cleavage, while malicious bots might favor amplification of the diffusion of non-credible information. Although the basic influence of information diffusion could be larger in human users than bots, the effects of bots are non-negligible under an infodemic situation.