Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811295 | C2 | semidirect |
| 2. #16811013 | C2 | semidirect |
| 3. #16810997 | C2 | semidirect |
| 4. #16810835 | C2 | semidirect |
| 5. #16810825 | C2 | semidirect |
| 6. #16810823 | C2 | semidirect |
| 7. #16810818 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 9. #16810721 | C2 | semidirect |
| 10. C4×#11719922 | C2 | semidirect |
| 11. C53×#556 | C2 | semidirect |
| 106. #88322 | #41 | semidirect |
| 133. #556 | D53 | semidirect |
| 144. C53 | #3397 | semidirect |