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I would like to know if every finite group is an extension of some group by another. Thanks

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    Every group is an extension of itself by the trivial group. Or, do you mean something else?2012-06-08
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    Or of the trivial group by itself. =]2012-06-08
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    The group with one element is an extension of itself by itself, but that is not very interesting. A group with two elements is an extension of itself by a group of one element, but that is still not very interesting. To be an interesting extension, it must have a normal subgroup that has more than one element, but not all of the elements. The groups that are not interesting extensions are called simple groups.2012-06-08
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    @Jack: I think that would probably do for an answer (perhaps including an example of a simple group).2012-06-08

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