中文摘要：

称有限群G的Cayley图r是正规Cayley图，如果G的右正则表示R（G）正规于图Г的全自同构群Aut（Г）。研究了三类2q2P阶亚循环群的连通3度Cayley图的正规性，其中q〈p均为奇素数，且q｜（p-1）。作为应用，决定了其中两类亚循环群的弱3-CI性。值得一提的是，在此用到单群分类定理。

英文摘要：

A Cayley （di）graph Г of a finite group G is said to be normal if the action of G on V（Г） by right multiplieation is normal in the full automor-phism group of Г. This paper mainly researehes the mormality of connected cubic Cayley graphs on three kinds of metacyclic groups with order 2q2p,where both q〈p are odd primes and q ｜（p-1）. In application,the weak 3-CI property of two kinds of groups are determined. The conclusion also involves in the classification of the finite simple groups.