Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16811423 | C2 | semidirect |
| 2. C2×#13133243 | C2 | semidirect |
| 3. C2×#13133243 | C2 | semidirect |
| 4. #16811389 | C2 | semidirect |
| 5. #16810892 | C2 | semidirect |
| 6. #16810885 | C2 | semidirect |
| 7. #16810671 | C2 | semidirect |
| 8. #16810605 | C2 | semidirect |
| 9. C2×#100×C53 | C2 | semidirect |
| 13. #13133250 | C22 | semidirect |
| 15. #13133245 | C22 | semidirect |
| 22. C2×#11719923 | C22 | semidirect |
| 24. C2×#11719922 | C22 | semidirect |
| 25. #13133225 | C22 | semidirect |
| 30. #13133152 | C22 | semidirect |
| 31. #13133135 | C22 | semidirect |
| 32. #13133133 | C22 | semidirect |
| 36. #100×C53 | C22 | semidirect |
| 156. C2×#100 | D53 | semidirect |
| 157. C53 | #3068 | semidirect |
| 184. #100 | C2×D53 | semidirect |