Races refer to visible differences in physical characteristics that define one as kin or non-kin, and causes us to respond according to our sensitivity to kin selection.
We generally divide people in to major races (four), sub-races (at least thirty), and then into regional or tribal groups, and then into clan, groups.
So the axis of decidability in race is kin selection: demonstration of genetic affiliation in association, cooperation, reproduction, production, politics, ‘religion’, and war.
By contrast, a ‘population group’ is a political and demographic term, invented in the era of ‘political correctness’ as an alternative to the use of the word ‘race’ or ‘subrace’, or ‘mixed race’ primarily because of crossbreeding that is producing various overlapping subgroups in this period of world migrations. It is not a term that refers to the demonstration of kin selection behavior by humans (and all other animals).
So as far as I know “population group” is a catch all term for the current era and the correct terminology for any subset would simply be “population sub group”, or whatever variation you feel you audience would comprehend. And I would recommend resisting the temptation to creative terminology that attempts to add scientific categorization for that which we cannot currently categorize.