darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p, where $p$ is a prime number, sci. china math., 56 (1) (2013) 213-219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$. in this paper we continue this work by classifying the connected cayley graph of groups of order...