Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #16811351 | C2 | semidirect |
| 3. #16810996 | C2 | semidirect |
| 4. #16810994 | C2 | semidirect |
| 5. #16810828 | C2 | semidirect |
| 6. #16810827 | C2 | semidirect |
| 7. #16810823 | C2 | semidirect |
| 8. #16810822 | C2 | semidirect |
| 9. C8×Dic106 | C2 | semidirect |
| 10. #16810710 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 102. Dic106 | SD16 | semidirect |
| 104. C8×C53 | #41 | semidirect |
| 139. C4×SD16 | D53 | semidirect |
| 140. C53 | #3392 | semidirect |
| 234. C8 | #11719945 | semidirect |