Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#13133239 | C2 | semidirect |
| 2. C2×D8×D53 | C2 | semidirect |
| 3. #16811270 | C2 | semidirect |
| 4. #16811006 | C2 | semidirect |
| 5. #16810865 | C2 | semidirect |
| 6. #16810837 | C2 | semidirect |
| 7. #16810775 | C2 | semidirect |
| 8. #16810766 | C2 | semidirect |
| 9. #16810705 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C53×#466 | C2 | semidirect |
| 12. C2×#11719945 | C22 | semidirect |
| 15. C2×Dic212 | C22 | semidirect |
| 16. C2×#11719913 | C22 | semidirect |
| 17. C2×#11719923 | C22 | semidirect |
| 22. #13133204 | C22 | semidirect |
| 27. #13133179 | C22 | semidirect |
| 30. #13133146 | C22 | semidirect |
| 31. #13133140 | C22 | semidirect |
| 32. #13133137 | C22 | semidirect |
| 33. C22⋊#88322 | C22 | semidirect |
| 35. C8×Dic53 | C22 | semidirect |
| 37. C22×C8×C53 | C22 | semidirect |
| 38. #121×C53 | C22 | semidirect |
| 39. #107×C53 | C22 | semidirect |
| 40. #102×C53 | C22 | semidirect |
| 77. D424 | D4 | semidirect |
| 127. C2×D53 | #135 | semidirect |
| 149. #466 | D53 | semidirect |
| 155. C53 | #3280 | semidirect |
| 167. C22×C8 | C2×D53 | semidirect |
| 172. #121 | C2×D53 | semidirect |
| 177. #107 | C2×D53 | semidirect |
| 181. #102 | C2×D53 | semidirect |