Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×#11719922 | C2 | semidirect |
| 2. C2×#13133224 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16810874 | C2 | semidirect |
| 5. #16810857 | C2 | semidirect |
| 6. #16810659 | C2 | semidirect |
| 7. #16810628 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C53×#535 | C2 | semidirect |
| 16. C2×#11719917 | C22 | semidirect |
| 18. C22×#88322 | C22 | semidirect |
| 21. #13133191 | C22 | semidirect |
| 24. #13133150 | C22 | semidirect |
| 25. #13133148 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 27. #13133137 | C22 | semidirect |
| 32. #121×C53 | C22 | semidirect |
| 67. C2×#88322 | D4 | semidirect |
| 129. #535 | D53 | semidirect |
| 135. C53 | #3058 | semidirect |
| 152. #121 | C2×D53 | semidirect |