The only examples I have seen have had an alternating group in the composition series.
What's an example of an unsolvable finite group without an alternating group in its composition series?
3
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abstract-algebra
group-theory
galois-theory
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2The smallest if the group $L_3(2) \cong L_2(7)$ of order 168. It is isomorphic to the multiplicative group of $3 \times 3$ non-singular matrices with entries in the finite field of order 2. – 2012-04-10