Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13133243 | C2 | semidirect |
| 2. C2×#13133223 | C2 | semidirect |
| 3. #16811204 | C2 | semidirect |
| 4. #16811190 | C2 | semidirect |
| 5. #16810875 | C2 | semidirect |
| 6. #16810868 | C2 | semidirect |
| 7. #16810858 | C2 | semidirect |
| 8. #16810851 | C2 | semidirect |
| 9. #16810663 | C2 | semidirect |
| 10. #16810620 | C2 | semidirect |
| 11. C2×#102×C53 | C2 | semidirect |
| 19. C2×#11719912 | C22 | semidirect |
| 20. C2×C8×D53 | C22 | semidirect |
| 24. #13133197 | C22 | semidirect |
| 26. #13133192 | C22 | semidirect |
| 32. #13133150 | C22 | semidirect |
| 33. #13133148 | C22 | semidirect |
| 34. #13133142 | C22 | semidirect |
| 35. #13133142 | C22 | semidirect |
| 36. #13133139 | C22 | semidirect |
| 37. #13133139 | C22 | semidirect |
| 81. #11719917 | D4 | semidirect |
| 162. C2×#102 | D53 | semidirect |
| 163. C53 | #3062 | semidirect |