This paper presents to integrate the auxiliary information (e.g., additional attributes for data such as the hashtags for Instagram images) in the self-supervised learning process. We first observe that the auxiliary information may bring us useful information about data structures: for instance, the Instagram images with the same hashtags can be semantically similar. Hence, to leverage the structural information from the auxiliary information, we present to construct data clusters according to the auxiliary information. Then, we introduce the Clustering InfoNCE (Cl-InfoNCE) objective that learns similar representations for augmented variants of data from the same cluster and dissimilar representations for data from different clusters. Our approach contributes as follows: 1) Comparing to conventional self-supervised representations, the auxiliary-information-infused self-supervised representations bring the performance closer to the supervised representations; 2) The presented Cl-InfoNCE can also work with unsupervised constructed clusters (e.g., k-means clusters) and outperform strong clustering-based self-supervised learning approaches, such as the Prototypical Contrastive Learning (PCL) method; 3) We show that Cl-InfoNCE may be a better approach to leverage the data clustering information, by comparing it to the baseline approach - learning to predict the clustering assignments with cross-entropy loss. For analysis, we connect the goodness of the learned representations with the statistical relationships: i) the mutual information between the labels and the clusters and ii) the conditional entropy of the clusters given the labels.