Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#13133245 | C2 | semidirect |
| 2. C2×#13133225 | C2 | semidirect |
| 3. #16811204 | C2 | semidirect |
| 4. #16811192 | C2 | semidirect |
| 5. #16810877 | C2 | semidirect |
| 6. #16810870 | C2 | semidirect |
| 7. #16810860 | C2 | semidirect |
| 8. #16810853 | C2 | semidirect |
| 9. #16810617 | C2 | semidirect |
| 10. C2×#13133137 | C2 | semidirect |
| 11. C53×#428 | C2 | semidirect |
| 19. C2×#11719912 | C22 | semidirect |
| 21. C2×C8×D53 | C22 | semidirect |
| 25. #13133197 | C22 | semidirect |
| 29. #13133192 | C22 | semidirect |
| 32. #13133140 | C22 | semidirect |
| 33. #13133140 | C22 | semidirect |
| 36. #13133137 | C22 | semidirect |
| 37. #13133137 | C22 | semidirect |
| 41. #107×C53 | C22 | semidirect |
| 42. #106×C53 | C22 | semidirect |
| 65. M16×C53 | D4 | semidirect |
| 160. #428 | D53 | semidirect |
| 163. C53 | #3062 | semidirect |
| 187. #107 | C2×D53 | semidirect |
| 188. #106 | C2×D53 | semidirect |
| 220. M16 | D212 | semidirect |