The number of conjugacy classes of non-normal cyclic subgroups in nilpotent groups of odd order

Let G be a nilpotent group of odd order, let c(G) denote the nilpotency class of G and let v*(G) denote the number of conjugacy classes of non-normal cyclic subgroups of G. Then c(G) less than or equal to v*(G) + 1, with equality if and only if either G is abelian or G = [a, b \ a(Pn) = b(P) = 1, a(b) = a(1+pn-1)] where p is an odd prime and n greater than or equal to 2. Examples show that this inequality need not hold for groups of even order.