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)

N{\lhd}G\}$. 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

group of order 36 in the small group library of GAP, a metabelian group of order

, in which n is odd positive integer and

is a Mersenne prime or a metabelian group of order

, where 3

n and

is a Mersenne prime. Moreover, we calculate the set

, for some finite group G.