Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16811330 | C2 | semidirect |
| 3. #16810970 | C2 | semidirect |
| 4. #16810942 | C2 | semidirect |
| 5. #16810914 | C2 | semidirect |
| 6. #16810852 | C2 | semidirect |
| 7. #16810824 | C2 | semidirect |
| 8. #16810776 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. C2×#13133139 | C2 | semidirect |
| 11. C8×D4×C53 | C2 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 16. #13133217 | C22 | semidirect |
| 19. #13133196 | C22 | semidirect |
| 24. C4×Dic106 | C22 | semidirect |
| 27. C2×C4⋊Dic53 | C22 | semidirect |
| 28. #13133149 | C22 | semidirect |
| 29. #13133149 | C22 | semidirect |
| 30. #13133142 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 35. #13133139 | C22 | semidirect |
| 36. C22×C8×C53 | C22 | semidirect |
| 38. C4⋊C8×C53 | C22 | semidirect |
| 39. C22⋊C8×C53 | C22 | semidirect |
| 40. C4×C8×C53 | C22 | semidirect |
| 83. D4×C53 | SD16 | semidirect |
| 146. C8×D4 | D53 | semidirect |
| 148. C53 | #3295 | semidirect |
| 153. C22×C8 | C2×D53 | semidirect |
| 169. C4⋊C8 | C2×D53 | semidirect |
| 176. C22⋊C8 | C2×D53 | semidirect |
| 177. C4×C8 | C2×D53 | semidirect |
| 231. D4 | #11719913 | semidirect |