To achieve this (currently) you must create multiple questions each with a specific filter for the possible value in the column or columns you want to group by. Then add these questions to a dashboard as a table display. I'm well aware that this 'limitation' is related to how SQL databases return results when GROUP BY is used.
Before I open a feature request I would like to get some input on the idea (if it's been considered) and what the correct "name" for it is.
The process to achieve this end result when "asking a question" in Metabase should be as simple as clicking "summarize", have an option to leave "summarize by" empty, then choosing the group by columns. Metabase should then be smart enough to run multiple queries to generate multiple tables. One table showing the results for each of the possible values for the selected column.