Group recommendation provides personalized recommendations to a group of users based on their shared interests, preferences, and characteristics. Current studies have explored different methods for integrating individual preferences and making collective decisions that benefit the group as a whole. However, most of them heavily rely on users with rich behavior and ignore latent preferences of users with relatively sparse behavior, leading to insufficient learning of individual interests. To address this challenge, we present the Multi-Granularity Attention Model (MGAM), a novel approach that utilizes multiple levels of granularity (i.e., subsets, groups, and supersets) to uncover group members' latent preferences and mitigate recommendation noise. Specially, we propose a Subset Preference Extraction module that enhances the representation of users' latent subset-level preferences by incorporating their previous interactions with items and utilizing a hierarchical mechanism. Additionally, our method introduces a Group Preference Extraction module and a Superset Preference Extraction module, which explore users' latent preferences on two levels: the group-level, which maintains users' original preferences, and the superset-level, which includes group-group exterior information. By incorporating the subset-level embedding, group-level embedding, and superset-level embedding, our proposed method effectively reduces group recommendation noise across multiple granularities and comprehensively learns individual interests. Extensive offline and online experiments have demonstrated the superiority of our method in terms of performance.