Self-supervised learning (SSL) is a powerful tool in machine learning, but understanding the learned representations and their underlying mechanisms remains a challenge. This paper presents an in-depth empirical analysis of SSL-trained representations, encompassing diverse models, architectures, and hyperparameters. Our study reveals an intriguing aspect of the SSL training process: it inherently facilitates the clustering of samples with respect to semantic labels, which is surprisingly driven by the SSL objective's regularization term. This clustering process not only enhances downstream classification but also compresses the data information. Furthermore, we establish that SSL-trained representations align more closely with semantic classes rather than random classes. Remarkably, we show that learned representations align with semantic classes across various hierarchical levels, and this alignment increases during training and when moving deeper into the network. Our findings provide valuable insights into SSL's representation learning mechanisms and their impact on performance across different sets of classes.