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×#13133243 | C2 | semidirect |
| 2. C2×#13133224 | C2 | semidirect |
| 3. #16811201 | C2 | semidirect |
| 4. #16810874 | C2 | semidirect |
| 5. #16810867 | C2 | semidirect |
| 6. #16810857 | C2 | semidirect |
| 7. #16810850 | C2 | semidirect |
| 8. #16810666 | C2 | semidirect |
| 9. #16810617 | C2 | semidirect |
| 10. C2×#13133138 | C2 | semidirect |
| 11. C53×#535 | C2 | semidirect |
| 18. C2×#11719917 | C22 | semidirect |
| 20. C22×#88322 | C22 | semidirect |
| 21. #13133196 | C22 | semidirect |
| 23. #13133191 | C22 | semidirect |
| 27. #13133150 | C22 | semidirect |
| 28. #13133148 | C22 | semidirect |
| 29. #13133140 | C22 | semidirect |
| 30. #13133140 | C22 | semidirect |
| 33. #13133137 | C22 | semidirect |
| 34. #13133137 | C22 | semidirect |
| 79. #11719917 | D4 | semidirect |
| 155. #535 | D53 | semidirect |
| 163. C53 | #3062 | semidirect |