Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16811345 | C2 | semidirect |
| 4. #16811001 | C2 | semidirect |
| 5. #16810848 | C2 | semidirect |
| 6. #16810845 | C2 | semidirect |
| 7. #16810827 | C2 | semidirect |
| 8. C8×Dic106 | C2 | semidirect |
| 9. #16810717 | C2 | semidirect |
| 11. C4×Q16×C53 | C2 | semidirect |
| 124. C4×Q16 | D53 | semidirect |
| 126. C53 | #3393 | semidirect |