Another group theory problem - not a proof cayley graphs

E3.2: For each of the following, draw the Cayley graph Γ(G,{a}), and use this to compute the order |a| of a, and to determine whether or not G = ⟨ {a} ⟩. Also find all of the subgroups of G of order 2.

I think I figured this out but I am not sure what the last part of the question is asking in regards the subgroups of G

###(a) G = U(18), a=5.

Cayley Graph: Γ(U(18),{5})

1 ----> 5 ----> 7 ----> 17 ----> 13 ----> 11 ---> back to 1

|5| = 6 Yes, G = ⟨ 5 ⟩.

###(b) G = U(18), a=7.

Cayley Graph: Γ(U(18),{7})

1 ----> 7 ----> 17---> back to 1

Order of |7| = 3 No, G = ⟨ 7 ⟩