Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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×#13133248 | C2 | semidirect |
| 2. C22×#11719924 | C2 | semidirect |
| 4. #16810845 | C2 | semidirect |
| 5. #16810823 | C2 | semidirect |
| 6. #16810650 | C2 | semidirect |
| 7. #16810627 | C2 | semidirect |
| 8. #16810617 | C2 | semidirect |
| 9. C53×#519 | C2 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 23. C4⋊#88322 | C22 | semidirect |
| 24. #13133140 | C22 | semidirect |
| 26. #13133137 | C22 | semidirect |
| 29. C4×Q8×C53 | C22 | semidirect |
| 36. C2×Q8×C53 | D4 | semidirect |
| 120. #519 | D53 | semidirect |
| 126. C53 | #3043 | semidirect |
| 142. C4×Q8 | C2×D53 | semidirect |
| 156. C2×Q8 | D212 | semidirect |