Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×#11719913 | C2 | semidirect |
| 2. C2×#13133223 | C2 | semidirect |
| 3. #16811199 | C2 | semidirect |
| 5. #16810870 | C2 | semidirect |
| 6. #16810853 | C2 | semidirect |
| 7. #16810631 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C53×#427 | C2 | semidirect |
| 18. C2×#11719912 | C22 | semidirect |
| 19. C2×C8×D53 | C22 | semidirect |
| 25. #13133197 | C22 | semidirect |
| 28. #13133140 | C22 | semidirect |
| 33. #107×C53 | C22 | semidirect |
| 34. #106×C53 | C22 | semidirect |
| 53. C2×C8×C53 | D4 | semidirect |
| 127. #427 | D53 | semidirect |
| 130. C53 | #3057 | semidirect |
| 152. #107 | C2×D53 | semidirect |
| 153. #106 | C2×D53 | semidirect |
| 180. C2×C8 | D212 | semidirect |