Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16811155 | C2 | semidirect |
| 2. #16811024 | C2 | semidirect |
| 3. #16811006 | C2 | semidirect |
| 4. #16810976 | C2 | semidirect |
| 5. #16810865 | C2 | semidirect |
| 7. #16810851 | C2 | semidirect |
| 8. C4×Dic212 | C2 | semidirect |
| 9. C4×#11719923 | C2 | semidirect |
| 10. C4×C8×D53 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 128. C4×D8 | D53 | semidirect |
| 130. C53 | #3168 | semidirect |