I am revising for my group theory exam and am trying to work the composition series for the Alternating Group $A_4$. I think if we let;
$N_1 = \, \langle(1 2)(3 4)\,,\, (1 3)(2 4)\rangle \quad\text{and}\quad \hspace{7pt} N_2 = \, \langle (1 3)(2 4)\rangle$ then we have a composition series
$ 1 \, \unlhd \, N_2 \unlhd \, N_1 \,\unlhd \,A_4$.
But I am not sure what the other ones are? How many are there in total?