Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
616 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×C8×D53 | C2 | semidirect |
| 3. C2×#13133192 | C2 | semidirect |
| 4. C2×#13133188 | C2 | semidirect |
| 5. #16810858 | C2 | direct (N × H) |
| 6. C2×#13133150 | C2 | semidirect |
| 7. C2×#13133139 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 14. C2×#11719922 | C22 | semidirect |
| 17. C2×C8×D53 | C22 | semidirect |
| 19. #13133192 | C22 | semidirect |
| 21. #13133188 | C22 | semidirect |
| 25. #13133150 | C22 | semidirect |
| 26. #13133139 | C22 | semidirect |
| 30. #102×C53 | C22 | semidirect |
| 63. C2×#88322 | D4 | semidirect |
| 77. C22×D53 | D8 | semidirect |
| 101. #88322 | C2×D4 | semidirect |
| 117. C2×D53 | C2×D8 | semidirect |
| 126. C2×C53 | #466 | semidirect |
| 139. C2×#102 | D53 | semidirect |
| 140. C53 | C2×#466 | semidirect |
| 162. #102 | C2×D53 | semidirect |
| 259. C2 | #16810858 | direct (N × H) |