This is a bit puzzling.
Sticking to point groups:
P3 & P6 are sub groups of P6/mmm so data which merges in P6/mmm will always satisfy P3 and P6.
And twinning in P3 or P6 will make the data seem to have higher symmetry.
Four way twinning is unusual, but possible of course.
But if you really have twinning, you should see it indicated in the pointless/aimless plots, or via Xtriage.. If those tests do not show it and you dont have a non-crystallographic translation twinning is unlikely.
Your choice of SGs seem puzzling too.
If the data is P31 (or P32) then you should see intensities for l=3n, and absences for l=3n+-1