Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16811251 | C2 | semidirect |
| 3. #16810925 | C2 | semidirect |
| 4. #16810921 | C2 | semidirect |
| 5. #16810911 | C2 | semidirect |
| 6. #16810901 | C2 | semidirect |
| 7. #16810665 | C2 | semidirect |
| 8. #16810659 | C2 | semidirect |
| 9. #16810651 | C2 | semidirect |
| 14. #13133216 | C22 | semidirect |
| 16. #13133208 | C22 | semidirect |
| 26. #13133151 | C22 | semidirect |
| 27. #13133150 | C22 | semidirect |
| 28. #13133150 | C22 | semidirect |
| 29. #13133149 | C22 | semidirect |
| 30. #13133148 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133146 | C22 | semidirect |
| 44. C2×D4×C53 | Q8 | semidirect |
| 136. C53 | #3081 | semidirect |
| 170. C2×D4 | Dic106 | semidirect |