Calculating number of subgroups of explicit order in Magma Calculator

Question

I have a group, given by direct product of $A_4$ and $D_6$. The exercise is to find all p-Sylow subgroups of $A_4 \times D_6$ without the use of 3rd Sylow theorem. I am confident I can find the subgroups, but I would like to know how many of them there are for each order, so that I don't necessarily have to do all the conjugations (using 2nd Sylow theorem) and to be sure of the findings. Is there a way to obtain that information in Magma Calculator, or perhaps an easier way to list all of the subgroups?

Answer 1

G := DirectProduct(AlternatingGroup(4), DihedralGroup(6));
Subgroups(G : OrderEqual := n);

Should do the trick. It will give you a representative from each conjugacy class of subgroups of order $n$, plus tell the number of subgroups in that conjugacy class (as the Length of the class).