|$ Z_12\oplus Z_4\oplus Z_15 $| = lcm(12,4,15) =60. Let G = $ Z_12\oplus Z_4\oplus Z_15 $, and H be a subgroup of G with |H|=9. By Lagrange's theorem, if H is a subgroup of G, then |H| divides |G|; however, 9 does not divide 60, therefore there is no such subgroup.
