In this article, we study the conditional structural connectivity of the alternating group graphs \(AG_n\) . We propose that if we remove multiple \(C_6\) from an alternating group graph \(AG_n\) , and then study the connectivity properties on \(AG_n\) . We show that if we remove \(n-3\) cycles of length being 6, the alternating group graph \(AG_n\) will be disconnected. Moreover, at least one of the remaining connected subgraphs is isomorphic to a cycle of length being 3.