Set X = fM11; M12; M22; M23; M24; Zn; T4n; SD8n; Sz(q); G2(q); V8ng, where M11, M12, M22, M23, M24 are Mathieu groups and Zn, T4n, SD8n, Sz(q), G2(q) and V8n denote the cyclic, dicyclic, semi-dihedral, Suzuki, Ree and a group of order 8n presented by V8n = ha; b j a2n = b4 = e; aba = b 1; ab 1a = bi; respectively. In this paper, we compute all eigenvalues of Cay(G; T), where G 2 X and T is minimal, second minimal, maximal or second maximal normal subset of G n feg with respect to its size. In the case that S is a minimal normal subset of G n feg, the summation of the absolute value of eigenvalues, energy of the CAYLEY GRAPH, is evaluated.