Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #16811421 | C2 | semidirect |
| 2. C2×#13133245 | C2 | semidirect |
| 3. C2×#13133242 | C2 | semidirect |
| 4. #16810893 | C2 | semidirect |
| 5. #16810886 | C2 | semidirect |
| 6. #16810672 | C2 | semidirect |
| 7. #16810605 | C2 | semidirect |
| 8. C2×#13133133 | C2 | semidirect |
| 9. C53×#568 | C2 | semidirect |
| 13. #13133247 | C22 | semidirect |
| 19. #13133242 | C22 | semidirect |
| 21. C2×#11719913 | C22 | semidirect |
| 23. C2×D424 | C22 | semidirect |
| 27. #13133153 | C22 | semidirect |
| 28. #13133135 | C22 | semidirect |
| 29. #13133133 | C22 | semidirect |
| 30. #13133133 | C22 | semidirect |
| 33. #131×C53 | C22 | semidirect |
| 151. #568 | D53 | semidirect |
| 157. C53 | #3068 | semidirect |
| 175. #131 | C2×D53 | semidirect |