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×#13133242 | C2 | semidirect |
| 2. C2×#13133223 | C2 | semidirect |
| 3. #16811201 | C2 | semidirect |
| 4. #16811192 | C2 | semidirect |
| 5. #16810875 | C2 | semidirect |
| 6. #16810872 | C2 | semidirect |
| 7. #16810858 | C2 | semidirect |
| 8. #16810855 | C2 | semidirect |
| 9. #16810666 | C2 | semidirect |
| 10. C2×#13133139 | C2 | semidirect |
| 11. C53×#416 | C2 | semidirect |
| 19. C2×#11719912 | C22 | semidirect |
| 20. C2×C8×D53 | C22 | semidirect |
| 24. #13133193 | C22 | semidirect |
| 29. #13133188 | C22 | semidirect |
| 32. #13133150 | C22 | semidirect |
| 33. #13133148 | C22 | semidirect |
| 39. #103×C53 | C22 | semidirect |
| 40. #103×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 42. #102×C53 | C22 | semidirect |
| 81. #11719917 | D4 | semidirect |
| 161. #416 | D53 | semidirect |
| 163. C53 | #3062 | semidirect |
| 189. #103 | C2×D53 | semidirect |
| 190. #103 | C2×D53 | semidirect |
| 193. #102 | C2×D53 | semidirect |
| 194. #102 | C2×D53 | semidirect |