ABSTRACT: Let G be a group and ω(G) be the set of element orders of G. Let k∈ω(G) and sk be the number of elements of order k in G. Let nse(G)={sk | k∈ω(G)}. L3(2)≅L2(7) is uniquely determined by nse(G). In this paper, we prove that if G is a group such that nse(G)=nse(L3(4)), then G≅L3(4).