A classification of tetravalent non-normal Cayley graphs of order twice a prime square

A Cayley graph $$\mathrm{Cay}(G, S)$$ on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of $$\mathrm{Cay}(G, S)$$ . In this paper, a complete classification is given of tetravalent non-normal Cayley graphs of order $$2p^2$$ for each prime p.