Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G};=;{ncc(N)$mid$N{lhd}G}$</TEX>. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{frac{n-1}{2}};-;1)$, in which n is odd positive integer and $2{frac{n-1}{2}};-;1$ is a Mersenne prime or a metabelian group of order $2^n(2{frac{n}{3}};-;1)$, where 3$mid$n and $2frac{n}{3};-;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.