I have this problem:

Let Y = {a, b, c, d} and let X = Sym(Y)

(a) Find cyclic subgroups of X of order 4:

my answer: (a)(b)(c)(d), (a)(c)(cd), (a)(bc)(d), (a)(bcd). (Correct?)

This part I need a little help with:

(b) Show that X has subgroup L which is isomorphic to the symetric group on a set with 3 elements...

Not sure how to start.