Clustering has been extensively studied in centralized settings, but relatively unexplored in federated ones that data are distributed among multiple clients and can only be kept local at the clients. The necessity to invest more resources in improving federated clustering methods is twofold: 1) The performance of supervised federated learning models can benefit from clustering. 2) It is non-trivial to extend centralized ones to perform federated clustering tasks. In centralized settings, various deep clustering methods that perform dimensionality reduction and clustering jointly have achieved great success. To obtain high-quality cluster information, it is natural but non-trivial to extend these methods to federated settings. For this purpose, we propose a simple but effective federated deep clustering method. It requires only one communication round between the central server and clients, can run asynchronously, and can handle device failures. Moreover, although most studies have highlighted adverse effects of the non-independent and identically distributed (non-IID) data across clients, experimental results indicate that the proposed method can significantly benefit from this scenario.