Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #16811351 | C2 | semidirect |
| 3. #16811016 | C2 | semidirect |
| 5. #16810848 | C2 | semidirect |
| 6. #16810833 | C2 | semidirect |
| 7. #16810827 | C2 | semidirect |
| 9. #16810753 | C2 | semidirect |
| 10. #16810722 | C2 | semidirect |
| 11. C4×Q16×C53 | C2 | semidirect |
| 132. C4×Q16 | D53 | semidirect |
| 133. C53 | #3400 | semidirect |