Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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. #16811332 | C2 | semidirect |
| 2. #16811027 | C2 | semidirect |
| 3. #16811025 | C2 | semidirect |
| 4. #16811024 | C2 | semidirect |
| 5. #16810925 | C2 | semidirect |
| 6. #16810923 | C2 | semidirect |
| 7. #16810911 | C2 | semidirect |
| 8. C8×Dic106 | C2 | semidirect |
| 45. D8×C53 | Q8 | semidirect |
| 120. C53 | #3380 | semidirect |
| 154. D8 | Dic106 | semidirect |