15 groups of order 6723.
| SmallGroups | group |
|---|---|
| (6723, 1) | C81×C83 #20269581 |
| (6723, 2) | C92×C83 #20269582 |
| (6723, 3) | C32⋊C9×C83 #20269583 |
| (6723, 4) | C9⋊C9×C83 #20269584 |
| (6723, 5) | C3×C27×C83 #20269585 |
| (6723, 6) | C27⋊C3×C83 #20269586 |
| (6723, 7) | AΣL(1,𝔽27)×C83 #20269587 |
| (6723, 8) | #731×C83 #20269588 |
| (6723, 9) | #732×C83 #20269589 |
| (6723, 10) | #733×C83 #20269590 |
| (6723, 11) | C32×C9×C83 #20269591 |
| (6723, 12) | C3×H(3,𝔽3)×C83 #20269592 |
| (6723, 13) | C3×3−1+2×C83 #20269593 |
| (6723, 14) | #737×C83 #20269594 |
| (6723, 15) | C34×C83 #20269595 |