Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 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. C22×#11719922 | C2 | semidirect |
| 2. C2×#13133225 | C2 | semidirect |
| 3. #16811192 | C2 | semidirect |
| 4. #16811190 | C2 | semidirect |
| 5. #16810875 | C2 | semidirect |
| 6. #16810858 | C2 | semidirect |
| 7. #16810659 | C2 | semidirect |
| 8. #16810629 | C2 | semidirect |
| 9. C53×#418 | C2 | semidirect |
| 16. C2×#11719912 | C22 | semidirect |
| 18. C2×C8×D53 | C22 | semidirect |
| 23. #13133192 | C22 | semidirect |
| 24. #13133188 | C22 | semidirect |
| 28. #13133150 | C22 | semidirect |
| 29. #13133148 | C22 | semidirect |
| 30. #13133139 | C22 | semidirect |
| 34. #102×C53 | C22 | semidirect |
| 66. C2×#88322 | D4 | semidirect |
| 134. #418 | D53 | semidirect |
| 135. C53 | #3058 | semidirect |
| 160. #102 | C2×D53 | semidirect |