Cubic non-normal Cayley graphs of order 4p24p2

A Cayley graph Cay(G,S) on a group GG is said to be normal   if the right regular representation R(G)R(G) of GG is normal in the full automorphism group of Cay(G,S). In this paper all connected cubic non-normal Cayley graphs of order 4p24p2 are constructed explicitly for each odd prime pp. It is shown that there are three infinite families of cubic non-normal Cayley graphs of order 4p24p2 with pp odd prime. Note that a complete classification of cubic non-Cayley vertex-transitive graphs of order 4p24p2 was given in [K. Kutnar, D. Marus˘ic˘, C. Zhang, On cubic non-Cayley vertex-transitive graphs, J. Graph Theory 69 (2012) 77–95]. As a result, a classification of cubic vertex-transitive graphs of order 4p24p2 can be deduced.