Social networks have community structure, in which the network is composed of highly clustered subnetworks (communities) with sparse links between them. Such community structure is expected to affect information diffusion among individuals. This paper empirically investigates how the community structure of a social network among Twitter users affects cascading diffusion of retweets among them. The results show that the frequency of retweets between users who are in the same community is approximately two times that between users who are in different communities. In contrast, the results also show that tweets disseminated via inter-community retweets have future popularity about 1.5-fold that of tweets disseminated via intra-community retweets. By using this fact, we construct classifiers to predict the future popularity of tweets from community-based features as well as features related to influence of users and tweet contents. Our experimental results show that contrary to our expectations, community-based features have little contributions for predicting the future popularity of tweets. This paper discusses the implications of the counterintuitive result.