Co-saliency detection (CoSOD) aims at discovering the repetitive salient objects from multiple images. Two primary challenges are group semantics extraction and noise object suppression. In this paper, we present a unified Two-stage grOup semantics PropagatIon and Contrastive learning NETwork (TopicNet) for CoSOD. TopicNet can be decomposed into two substructures, including a two-stage group semantics propagation module (TGSP) to address the first challenge and a contrastive learning module (CLM) to address the second challenge. Concretely, for TGSP, we design an image-to-group propagation module (IGP) to capture the consensus representation of intra-group similar features and a group-to-pixel propagation module (GPP) to build the relevancy of consensus representation. For CLM, with the design of positive samples, the semantic consistency is enhanced. With the design of negative samples, the noise objects are suppressed. Experimental results on three prevailing benchmarks reveal that TopicNet outperforms other competitors in terms of various evaluation metrics.