Factorizing a finite group into conjugates of a subgroup

For every non-nilpotent finite group G, there exists at least one proper subgroup M such that G is the setwise product of a finite number of conjugates of M. We define γcp(G) to be the smallest number k such that G is a product, in some order, of k pairwise conjugated proper subgroups of G. We prove that if G is non-solvable then γcp(G)≤36 while if G is solvable then γcp(G) can attain any integer value bigger than 2, while, on the other hand, γcp(G)≤4log2⁡|G|.