Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #16811586 | C2 | semidirect |
| 4. C2×C8×#6157 | C2 | semidirect |
| 5. #16811498 | C2 | semidirect |
| 6. #16811495 | C2 | semidirect |
| 12. #13133282 | C4 | semidirect |
| 13. #13133281 | C4 | semidirect |
| 14. #13133280 | C4 | semidirect |
| 15. #13133279 | C4 | semidirect |
| 22. #13133225 | C4 | semidirect |
| 23. #13133224 | C4 | semidirect |
| 25. #13133223 | C4 | semidirect |
| 30. #131×C53 | C4 | semidirect |
| 135. C53 | #1764 | semidirect |
| 142. #131 | #6157 | semidirect |