Maximal Subgroups of Some Groups of Extension

Abstract

Let G be a finite group. A maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K of G strictly contains H. If N and G are groups, an extensionof N by G is a group M such that N⊴M and M/N≅G. In this paper, we determinegroups of extension and L3(3): 2 from some finitegroups using modular representation method. We determine the maximal subgroups from the group extensions. We determine the degree, order, number of orbits and the length of the orbits to classify the maximal subgroups obtained from groups of extension.