the one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups

We say that a group g satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers. insoluble groups which satisfy the one-prime power hypothesis have been classified. however it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups. in this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups.