Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16811176 | C2 | semidirect |
| 3. #16810979 | C2 | semidirect |
| 4. #16810976 | C2 | semidirect |
| 5. #16810972 | C2 | semidirect |
| 6. #16810968 | C2 | semidirect |
| 7. #16810620 | C2 | semidirect |
| 8. #16810619 | C2 | semidirect |
| 9. #16810617 | C2 | semidirect |
| 10. C2×C8×Dic53 | C2 | semidirect |
| 11. C53×#416 | C2 | semidirect |
| 135. #416 | D53 | semidirect |
| 137. C53 | #3131 | semidirect |