Clustering continues to be a significant and challenging task. Recent studies have demonstrated impressive results by applying clustering to feature representations acquired through self-supervised learning, particularly on small datasets. However, when dealing with datasets containing a large number of clusters, such as ImageNet, current methods struggle to achieve satisfactory clustering performance. In this paper, we introduce a novel method called Contrastive representation Disentanglement for Clustering (CDC) that leverages contrastive learning to directly disentangle the feature representation for clustering. In CDC, we decompose the representation into two distinct components: one component encodes categorical information under an equipartition constraint, and the other component captures instance-specific factors. To train our model, we propose a contrastive loss that effectively utilizes both components of the representation. We conduct a theoretical analysis of the proposed loss and highlight how it assigns different weights to negative samples during the process of disentangling the feature representation. Further analysis of the gradients reveals that larger weights emphasize a stronger focus on hard negative samples. As a result, the proposed loss exhibits strong expressiveness, enabling efficient disentanglement of categorical information. Through experimental evaluation on various benchmark datasets, our method demonstrates either state-of-the-art or highly competitive clustering performance. Notably, on the complete ImageNet dataset, we achieve an accuracy of 53.4%, surpassing existing methods by a substantial margin of +10.2%.