Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 1. D4×D212 | C2 | semidirect |
| 2. #16810971 | C2 | semidirect |
| 3. #16810947 | C2 | semidirect |
| 4. #16810910 | C2 | semidirect |
| 5. #16810874 | C2 | semidirect |
| 6. #16810818 | C2 | semidirect |
| 7. #16810756 | C2 | semidirect |
| 8. C4×#11719922 | C2 | semidirect |
| 9. #16810701 | C2 | semidirect |
| 10. #16810627 | C2 | semidirect |
| 11. C53×#555 | C2 | semidirect |
| 15. C2×#11719922 | C22 | semidirect |
| 16. C2×#11719917 | C22 | semidirect |
| 22. #13133150 | C22 | semidirect |
| 23. #13133148 | C22 | semidirect |
| 24. C4⋊#88322 | C22 | semidirect |
| 25. #13133138 | 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. #121×C53 | C22 | semidirect |
| 38. C4×D4×C53 | C22 | semidirect |
| 40. #117×C53 | C22 | semidirect |
| 141. #555 | D53 | semidirect |
| 152. C53 | #3325 | semidirect |
| 158. C4⋊Q8 | C2×D53 | semidirect |
| 164. #121 | C2×D53 | semidirect |
| 168. C4×D4 | C2×D53 | semidirect |
| 170. #117 | C2×D53 | semidirect |