16 groups of order 6724.
| SmallGroups | group |
|---|---|
| (6724, 1) | C4×C1681 #20269596 |
| (6724, 2) | Dic1681 #20269597 |
| (6724, 3) | C22×C1681 #20269598 |
| (6724, 4) | #20269599 |
| (6724, 5) | C2×D1681 #20269600 |
| (6724, 6) | C4×C412 #20269601 |
| (6724, 7) | C41×Dic41 #20269602 |
| (6724, 8) | #20269603 |
| (6724, 9) | C22×C412 #20269604 |
| (6724, 10) | C41×#4223 #20269605 |
| (6724, 11) | #20269606 |
| (6724, 12) | D412 #20269607 |
| (6724, 13) | #20269608 |
| (6724, 14) | #20269609 |
| (6724, 15) | C2×C41×D41 #20269610 |
| (6724, 16) | C2×C41⋊D41 #20269611 |