Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×#11719924 | C2 | semidirect |
| 2. C2×#13133224 | C2 | semidirect |
| 4. #16810871 | C2 | semidirect |
| 5. #16810854 | C2 | semidirect |
| 6. #16810659 | C2 | semidirect |
| 7. #16810632 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C53×#536 | C2 | semidirect |
| 16. C2×#11719917 | C22 | semidirect |
| 18. C22×#88322 | C22 | semidirect |
| 24. #13133150 | C22 | semidirect |
| 25. #13133148 | C22 | semidirect |
| 26. #13133141 | C22 | semidirect |
| 33. C22⋊Q8×C53 | C22 | semidirect |
| 67. C2×#88322 | D4 | semidirect |
| 123. #536 | D53 | semidirect |
| 130. C53 | #3057 | semidirect |
| 147. C22⋊Q8 | C2×D53 | semidirect |