On the number of the irreducible characters of factor groups

‎Let G be a finite group and let N be a normal subgroup of G‎. ‎Suppose that {\rm{Irr}} (G | N) is the set of the irreducible characters of G that contain N in their kernels‎. ‎In this paper‎, ‎we classify solvable groups G in which the set \mathcal{C} (G) = \{{\rm{Irr}} (G | N) | ۱ \ne N \trianglelefteq G \} has at most three elements‎. ‎We also compute the set \mathcal{C}(G) for such groups‎.