Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 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. #16811343 | C2 | semidirect |
| 3. #16811021 | C2 | semidirect |
| 4. #16810965 | C2 | semidirect |
| 5. #16810948 | C2 | semidirect |
| 6. #16810919 | C2 | semidirect |
| 7. #16810904 | C2 | semidirect |
| 8. #16810852 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. #16810661 | C2 | semidirect |
| 11. C8×D4×C53 | C2 | semidirect |
| 130. C8×D4 | D53 | semidirect |
| 132. C53 | #3340 | semidirect |