Direct product, semidirect product and central extension are different types of group extensions. Is there any other type? If there is, can you please give an example with a small finite group?
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Yes, there are other types, like non-central extensions, non-split extension, etc. Many examples can be found at this site. Have you searched already? – Dietrich Burde Jan 14 '21 at 12:46
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Yes, thank you! – user713320 Jan 14 '21 at 13:20