Direct product and Decomposition of a symmetric group
I am looking for a mechanism to find a decomposition of symmetric groups. For finitely generated abelian group G, there is a mechanism to decompose G such that G is isomorphic to a direct sum of cyclic groups.
For symmetric groups, it seems a bit complex for me to find it.
For example,
(1) is it possible for 
to be decomposed as a direct product of groups?
In more general cases, is there any mechanism to decompose 
as a direct product of groups?
(2) is there any mechanism to find an isomorphic group of a direct product of symmetric groups? Let's say,
Any isomorphic group of above G?
I can give you a cheesy isomophism
recall the dihedral group of order 6, 
in fact every non abelian group of order 6 is isomorphic. So 
