Size of A4 =12
So, there are either 1 or 3 2-sylow subgroups
and there are either 1 or 4 3-sylow subgroups.
Suppose that there are 4 3-sylow subgroups. Then, there are 8 elements of order 3
Thus, 2-sylow subgroup must be unique.
However, this is case when I suppose that there are 3-sylow subgroups.
What If I suppose that there are 2-sylow subgroups and derive the result that there can't be 4 3-sylow subgroups?
Also, How can I find the subgroup of order 4?
Do I have to look at every element in A4 and consider possible cases?