finding all composition series of ${\rm sym} \ (4)$ How can I find all composition series of ${\rm sym}\ (4)$ ? I think first I have to find all maximal normal subgroups. But how ? Thanks.
Without words:

$$1\lhd \{(1)\,,\,(12)(34)\}\lhd\{(1)\,,\,(12)(34)\,,\,(13)(24)\,,\,(14)(23)\}\lhd A_4\lhd     S_4$$
this isn't correct, since {(1),(12)(34)} is only a subgroup of A4, but isn't normal,
since a normal subgroup is a union of complete conjugacy classes, and elt (12)(34)
isn't a complete c.class. 

or, try conjugation of {(1),(12)(34)} by elt (123) (which is even) and you get 
{(1),(14)(23)} not ={(1),(12)(34)}. 

of course {(1),(12)(34)}⊲{(1),(12)(34),(13)(24),(14)(23)}
is true, since {(1),(12)(34),(13)(24),(14)(23)} is abelian, and every subgroup of
an abelian group is Normal, but {(1),(12)(34)} isn't normal in A4