Decentralized proactive caching and coded delivery is studied in a content delivery network, where each user is equipped with a cache memory, not necessarily of equal capacity. Cache memories are filled in advance during the off-peak traffic period in a decentralized manner, i.e., without the knowledge of the number of active users, their identities, or their particular demands. User demands are revealed during the peak traffic period, and are served simultaneously through an error-free shared link. The goal is to find the minimum delivery rate during the peak traffic period that is sufficient to satisfy all possible demand combinations. A group-based decentralized caching and coded delivery scheme is proposed, and it is shown to improve upon the state-of-the-art in terms of the minimum required delivery rate when there are more users in the system than files. Numerical results indicate that the improvement is more significant as the cache capacities of the users become more skewed. A new lower bound on the delivery rate is also presented, which provides a tighter bound than the classical cut-set bound.