Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#13133243 | C2 | semidirect |
| 2. C22×#11719922 | C2 | semidirect |
| 3. #16811192 | C2 | semidirect |
| 4. #16810838 | C2 | semidirect |
| 5. #16810818 | C2 | semidirect |
| 6. #16810650 | C2 | semidirect |
| 7. #16810627 | C2 | semidirect |
| 8. #16810617 | C2 | semidirect |
| 9. C53×#518 | C2 | semidirect |
| 13. C2×#11719923 | C22 | semidirect |
| 16. C2×#11719922 | C22 | semidirect |
| 19. #13133214 | C22 | semidirect |
| 20. #13133205 | C22 | semidirect |
| 23. C4⋊#88322 | C22 | semidirect |
| 24. #13133140 | C22 | semidirect |
| 25. #13133137 | C22 | semidirect |
| 26. #13133137 | C22 | semidirect |
| 29. C4×D4×C53 | C22 | semidirect |
| 37. C2×D4×C53 | D4 | semidirect |
| 125. #518 | D53 | semidirect |
| 131. C53 | #3041 | semidirect |
| 147. C4×D4 | C2×D53 | semidirect |
| 169. C2×D4 | D212 | semidirect |