Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×D424 | C2 | semidirect |
| 2. C2×#13133223 | C2 | semidirect |
| 3. #16811192 | C2 | semidirect |
| 4. #16810877 | C2 | semidirect |
| 5. #16810860 | C2 | semidirect |
| 6. #16810627 | C2 | semidirect |
| 7. C53×#427 | C2 | semidirect |
| 15. C2×#11719912 | C22 | semidirect |
| 16. C2×C8×D53 | C22 | semidirect |
| 19. #13133192 | C22 | semidirect |
| 21. #13133137 | C22 | semidirect |
| 24. #107×C53 | C22 | semidirect |
| 25. #106×C53 | C22 | semidirect |
| 39. C2×C8×C53 | D4 | semidirect |
| 99. #427 | D53 | semidirect |
| 101. C53 | #3058 | semidirect |
| 117. #107 | C2×D53 | semidirect |
| 118. #106 | C2×D53 | semidirect |
| 139. C2×C8 | D212 | semidirect |