The importance of Schur-Zassenhaus theorem

Question

I've just studied the Schur-Zassenhaus theorem (here there is the statement), but I don't understand its importance in the theory of finite groups. Wikipedia for example says:

The Schur–Zassenhaus theorem at least partially answers the question: "In a composition series, how can we classify groups with a certain set of composition factors?"

but for me it's not clear what does it means.

Answer 1

If you know the composition factors consist of the sequence of simple groups $H_1,...,H_n$ with the orders of the groups relatively prime, then you know that the original group must be some chained a chained semi-direct product of those simple groups.

It's certainly not extremely helpful, since the composition factors are simple groups, and the non-commutative simple groups are all of even order. so for this condition to hold, at most one of the $H_i$ can be non-commutative.