Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16811154 | C2 | semidirect |
| 2. C2×D4×Dic53 | C2 | semidirect |
| 3. #16810954 | C2 | semidirect |
| 4. #16810934 | C2 | semidirect |
| 5. #16810925 | C2 | semidirect |
| 6. #16810836 | C2 | semidirect |
| 7. #16810774 | C2 | semidirect |
| 8. #16810735 | C2 | semidirect |
| 9. #16810720 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 15. #13133208 | C22 | semidirect |
| 16. #13133204 | C22 | semidirect |
| 19. #13133182 | C22 | semidirect |
| 25. D4×Dic53 | C22 | semidirect |
| 30. #13133150 | C22 | semidirect |
| 31. #13133149 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 35. #13133138 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 152. C53 | #3114 | semidirect |