Automorphisms of cubic Cayley graphs of order 2pq2pq

In this paper the automorphism groups of connected cubic Cayley graphs of order 2pq2pq for distinct odd primes pp and qq are determined. As an application, all connected cubic non-symmetric Cayley graphs of order 2pq2pq are classified and this, together with classifications of connected cubic symmetric graphs and vertex-transitive non-Cayley graphs of order 2pq2pq given by the last two authors, completes a classification of connected cubic vertex-transitive graphs of order 2pq2pq.