Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 135 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. #16811176 | C2 | semidirect |
| 3. #16810926 | C2 | semidirect |
| 4. #16810922 | C2 | semidirect |
| 5. #16810912 | C2 | semidirect |
| 6. #16810902 | C2 | semidirect |
| 7. #16810663 | C2 | semidirect |
| 8. #16810646 | C2 | semidirect |
| 11. C53×#428 | C2 | semidirect |
| 15. #13133216 | C22 | semidirect |
| 16. #13133216 | C22 | semidirect |
| 17. #13133208 | C22 | semidirect |
| 18. #13133208 | C22 | semidirect |
| 30. #13133150 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133146 | C22 | semidirect |
| 41. #107×C53 | C22 | semidirect |
| 42. #106×C53 | C22 | semidirect |
| 50. C2×D212 | Q8 | semidirect |
| 146. #428 | D53 | semidirect |
| 150. C53 | #3077 | semidirect |
| 173. #107 | C2×D53 | semidirect |
| 175. #106 | C2×D53 | semidirect |