Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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. #16810947 | C2 | semidirect |
| 3. #16810947 | C2 | semidirect |
| 4. #16810941 | C2 | semidirect |
| 5. #16810936 | C2 | semidirect |
| 6. #16810663 | C2 | semidirect |
| 7. #16810659 | C2 | semidirect |
| 8. #16810627 | C2 | semidirect |
| 9. C2×#13133137 | C2 | semidirect |
| 10. #16810590 | C2 | semidirect |
| 11. C53×#520 | C2 | semidirect |
| 21. #13133150 | C22 | semidirect |
| 22. #13133150 | C22 | semidirect |
| 23. #13133150 | C22 | semidirect |
| 24. #13133148 | C22 | semidirect |
| 25. #13133148 | C22 | semidirect |
| 26. #13133148 | C22 | semidirect |
| 31. C22⋊#88322 | C22 | semidirect |
| 32. C22⋊#88322 | C22 | semidirect |
| 38. #117×C53 | C22 | semidirect |
| 40. C2×C4⋊C4×C53 | C22 | semidirect |
| 136. #520 | D53 | semidirect |
| 146. C53 | #3096 | semidirect |
| 161. #117 | C2×D53 | semidirect |
| 163. C2×C4⋊C4 | C2×D53 | semidirect |