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Deep clustering has attracted increasing attention in recent years due to its capability of joint representation learning and clustering via deep neural networks. In its latest developments, the contrastive learning has emerged as an effective technique to substantially enhance the deep clustering performance. However, the existing contrastive learning based deep clustering algorithms mostly focus on some carefully-designed augmentations (often with limited transformations to preserve the structure), referred to as weak augmentations, but cannot go beyond the weak augmentations to explore the more opportunities in stronger augmentations (with more aggressive transformations or even severe distortions). In this paper, we present an end-to-end deep clustering approach termed Strongly Augmented Contrastive Clustering (SACC), which extends the conventional two-augmentation-view paradigm to multiple views and jointly leverages strong and weak augmentations for strengthened deep clustering. Particularly, we utilize a backbone network with triply-shared weights, where a strongly augmented view and two weakly augmented views are incorporated. Based on the representations produced by the backbone, the weak-weak view pair and the strong-weak view pairs are simultaneously exploited for the instance-level contrastive learning (via an instance projector) and the cluster-level contrastive learning (via a cluster projector), which, together with the backbone, can be jointly optimized in a purely unsupervised manner. Experimental results on five challenging image datasets have shown the superiority of our SACC approach over the state-of-the-art. The code is available at https://github.com/dengxiaozhi/SACC.