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

Let p be a prime, and let Λ 2 p be a connected cubic arc-transitive graph of order 2 p . In the literature, a lot of works have been done on the classification of edge-transitive normal covers of Λ 2 p 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 Λ 2 p for each prime p . In our previous work, we classified all edge-transitive N -normal covers of Λ 2 p , 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 Λ 2 p , where p ≥ 5 is a prime and N is a metacyclic group of odd prime power order.