Summary: We consider the relationships between Cayley digraphs and their coset graphs with respect to subgroups and obtain some general results on homomorphism and broadcasting between them. We also derive a general factorization theorem on subgraphs of Cayley digraphs by their automorphism groups. We discuss the applications of these results to well-known interconnection networks such as the butterfly network, the de Bruijn network, the cube-connected cycles network and the shuffle-exchange network.