A sortable list of groups, or having multiple types of data on the same column

Sorry if the title’s vague, but I don’t know if there’s a word for the type of thing I’m trying to create. Allow me to illustrate with a picture:

Is it possible to create a spreadsheet consisting of groups of rows containing several different types of data, and be able to sort those groups according to any of the data within them without rearranging the contents of the groups themselves?

Merged cells will prevent you from sorting.

Tested with LibreOffice (x86); OS: Windows 6.1.

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