Recall the following: theorem: (lagrange's theorem) let g be a finite group and hcg. if h is a subgroup of g, then h| divides gl. the purpose of this exercise is to show that the converse of lagrange's theorem is not true in general. recall that al is not abelian, since (1 2), (23) e a4, but (1 2)(23) + (23)(1 2). (a) count the number of elements of order 3 in al. (b) for sake of contradiction, suppose there exists a subgroup hcaof order 6. i. explain why h must be normal in a4. ii. leto e ad have order 3. suppose that o h. arrive at a contradiction. iii. conclude that we must have o eh. arrive at another contradiction. (c) conclude that, although 6 divides the order of a4, as contains no subgroup of order 6.