Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16811333 | C2 | semidirect |
| 2. #16811028 | C2 | semidirect |
| 3. #16811025 | C2 | semidirect |
| 4. #16810924 | C2 | semidirect |
| 5. #16810914 | C2 | semidirect |
| 8. C8×Q8×C53 | C2 | semidirect |
| 47. D424 | Q8 | semidirect |
| 87. C8×Q8 | D53 | semidirect |
| 90. C53 | #3380 | semidirect |