simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime, it was shown by Folkman (J. Combin. Theory 3 (1967) 215-232) that a regular edge-transitive graph of order 2p or 2p2 is necessarily vertex-transitive. In this paper an extension of his result in the case of cubic graph is given. It is proved that, with the exception of the graph on 216 vertices, every cubic edge-transitive graph of order 8p3 is vertex-transitive
