If you have a four facing formation, you could do petronellas in two small groups of four; or petronellas in a big group of eight.
Four petronellas in groups of 4 returns everyone to their starting location. But four petronellas in a group of 8 would only get people halfway around; swapping everyone with their opposite.
The fun (or crazy) thing is combinations of small circle and big circle petronella.
If you started with a group
A B C D
H G F E
then a sequence of petronellas starting in small groups of 4, then all 8, then in small groups of four on the sides, then all 8 (which I’ll call 4-8-4-8) returns half the dancers to their original configuration but swaps the other half (bold dancers return to starting places)
A B C D 4-8-4-8 A F C H
H G F E D G B E
If our dancers were in standard 4 face 4 improper, that swaps the gents.
If we take a different sequence of petronella in a group of 8, then 4s, then 8, then 4s.
A B C D 8-4-8-4 E B G D
H G F E H C F A
Which swaps the women.
The other pemutations of equal numbers of big and little petronellas:
Can swap one couple on the diagonal and return the other couple
A B C D 8-8-4-4 A B G H
H G F E D C F E
A B C D 4-4-8-8 E F C D
H G F E H G B A
Or swap ends or middle
A B C D 8-4-4-8 A F G D
H G F E H C B E
A B C D 4-8-8-4 E B C H
H G F E D G F A
As to WHY you might need to work out these permutations (besides the joy of looking at group theory), I’ve used 4 petronellas as half of a new Tempest Formation dance, Bohrd with Models.