Which taxonomic group includes kingdoms and all other levels of taxonomy?

The most probable and the most likely answer that you would get in asking this question would be domain.

As for stating it as a taxonomic group, it is more appropriate to refer to it as category, but there is no arguing that both words can be interchanged so just take that as a personal preference. Domain would be referred to in modern taxonomic category as the category that includes the kingdoms and all the other levels of the taxonomic hierarchy.