Product of groups with different properties

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This is not a hint-to-solve-exercise question, but just mathematical curiosity involving one my favorites branches of this beautiful science: group theory. Having done some research in databases like this one, I came across with some different ways to construct groups of a given order. Since I don't know about extensions, my knowledge is more limited but I have a question: how many "different" group/subgroup products are there? In the database I wrote, I found things like "central product", "wreath product" (apart from the typical direct or semidirect ones), etc, but, are these products the only constructions? Am I missing other types of products?