Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16811346 | C2 | semidirect |
| 2. #16811333 | C2 | semidirect |
| 3. #16810978 | C2 | semidirect |
| 4. #16810974 | C2 | semidirect |
| 5. #16810931 | C2 | semidirect |
| 6. #16810914 | C2 | semidirect |
| 8. #16810829 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 11. C8×Q8×C53 | C2 | semidirect |
| 129. C8×Q8 | D53 | semidirect |
| 132. C53 | #3360 | semidirect |