We study self-supervised learning on graphs using contrastive methods. A general scheme of prior methods is to optimize two-view representations of input graphs. In many studies, a single graph-level representation is computed as one of the contrastive objectives, capturing limited characteristics of graphs. We argue that contrasting graphs in multiple subspaces enables graph encoders to capture more abundant characteristics. To this end, we propose a group contrastive learning framework in this work. Our framework embeds the given graph into multiple subspaces, of which each representation is prompted to encode specific characteristics of graphs. To learn diverse and informative representations, we develop principled objectives that enable us to capture the relations among both intra-space and inter-space representations in groups. Under the proposed framework, we further develop an attention-based representor function to compute representations that capture different substructures of a given graph. Built upon our framework, we extend two current methods into GroupCL and GroupIG, equipped with the proposed objective. Comprehensive experimental results show our framework achieves a promising boost in performance on a variety of datasets. In addition, our qualitative results show that features generated from our representor successfully capture various specific characteristics of graphs.