Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 2. #16810989 | C2 | semidirect |
| 3. #16810985 | C2 | semidirect |
| 4. #16810980 | C2 | semidirect |
| 5. #16810971 | C2 | semidirect |
| 6. #16810627 | C2 | semidirect |
| 7. #16810622 | C2 | semidirect |
| 8. #16810617 | C2 | semidirect |
| 9. C2×#13133137 | C2 | semidirect |
| 10. #16810579 | C2 | semidirect |
| 11. C53×#544 | C2 | semidirect |
| 21. #13133140 | C22 | semidirect |
| 22. #13133140 | C22 | semidirect |
| 23. #13133140 | C22 | semidirect |
| 28. #13133137 | C22 | semidirect |
| 29. #13133137 | C22 | semidirect |
| 30. #13133137 | C22 | semidirect |
| 31. #13133128 | C22 | semidirect |
| 32. C4×#88322 | C22 | semidirect |
| 34. C4⋊Q8×C53 | C22 | semidirect |
| 36. #125×C53 | C22 | semidirect |
| 136. #544 | D53 | semidirect |
| 147. C53 | #3136 | semidirect |
| 153. C4⋊Q8 | C2×D53 | semidirect |
| 156. #125 | C2×D53 | semidirect |