May I bring forth a suggestion? Why not name all the groups after planets (minus Earth and Uranus because nobody wants their group to be named Uranus) and the six groups could be considered sub-units of a large group called Milky Way?GROUP ONE
-Galaxy-
GROUP TWO
-Mercury-
GROUP THREE
-Venus-
GROUP FOUR
-Mars-
GROUP FIVE
-Jupiter-
GROUP SIX
-Saturn-
FANDOM NAME
-Stars-
Don't mind me I literally came up with this right before I went to bed last night.