A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex K. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In this talk I will give a formula for the fixed point set of the polyhedral product for any subgroup H of Aut(K) and explore the computation of Bredon cohomolohgy of the polyhedral product for small non-Abelian groups such as \(D_8\) and \(\Sigma_4\).