On edge-transitive metacyclic covers of cubic arc-transitive graphs of order twice a prime

Let p be a prime, and let Lambda(2p) be a connected cubic arc-transitive graph of order 2p. In the literature, a lot of works have been done on the classification of edge-transitive normal covers of Lambda(2p) for specific p <= 7. An interesting problem is to generalize these results to an arbitrary prime p. In 2014, Zhou and Feng classified edge-transitive cyclic or dihedral normal covers of Lambda(2p) for each prime p. In our previous work, we classified all edge-transitive N-normal covers of Lambda(2p), where p is a prime and N is a metacyclic 2-group. In this paper, we give a classification of edge-transitive N-normal covers of Lambda(2p), where p >= 5 is a prime and N is a metacyclic group of odd prime power order.