Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811358 | C2 | semidirect |
| 2. #16811346 | C2 | semidirect |
| 3. #16811007 | C2 | semidirect |
| 4. #16810996 | C2 | semidirect |
| 5. #16810846 | C2 | semidirect |
| 6. #16810839 | C2 | semidirect |
| 7. #16810834 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. C4×#11719913 | C2 | semidirect |
| 11. C8×Q8×C53 | C2 | semidirect |
| 134. C8×Q8 | D53 | semidirect |
| 137. C53 | #3394 | semidirect |