Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #16810971 | C2 | semidirect |
| 3. #16810947 | C2 | semidirect |
| 4. #16810900 | C2 | semidirect |
| 5. #16810871 | C2 | semidirect |
| 6. #16810823 | C2 | semidirect |
| 7. #16810773 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. #16810701 | C2 | semidirect |
| 10. #16810627 | C2 | semidirect |
| 11. C53×#556 | C2 | semidirect |
| 15. C2×#11719924 | C22 | semidirect |
| 16. C2×#11719917 | C22 | semidirect |
| 22. #13133150 | C22 | semidirect |
| 23. #13133148 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133141 | C22 | semidirect |
| 28. #13133137 | C22 | semidirect |
| 29. #13133137 | C22 | semidirect |
| 30. #13133137 | C22 | semidirect |
| 31. C22⋊#88322 | C22 | semidirect |
| 32. C4×#88322 | C22 | semidirect |
| 33. C4⋊Q8×C53 | C22 | semidirect |
| 36. C22⋊Q8×C53 | C22 | semidirect |
| 38. C4×Q8×C53 | C22 | semidirect |
| 40. #117×C53 | C22 | semidirect |
| 136. #556 | D53 | semidirect |
| 147. C53 | #3324 | semidirect |
| 153. C4⋊Q8 | C2×D53 | semidirect |
| 157. C22⋊Q8 | C2×D53 | semidirect |
| 162. C4×Q8 | C2×D53 | semidirect |
| 165. #117 | C2×D53 | semidirect |