Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811173 | C2 | semidirect |
| 2. #16811033 | C2 | semidirect |
| 3. #16811013 | C2 | semidirect |
| 4. #16810989 | C2 | semidirect |
| 5. #16810982 | C2 | semidirect |
| 6. #16810857 | C2 | semidirect |
| 7. #16810854 | C2 | semidirect |
| 8. #16810733 | C2 | semidirect |
| 9. #16810721 | C2 | semidirect |
| 10. C2×#13133128 | C2 | semidirect |
| 11. C53×#529 | C2 | semidirect |
| 110. #88322 | #41 | semidirect |
| 139. #529 | D53 | semidirect |
| 149. C53 | #3180 | semidirect |