Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811134 | C2 | semidirect |
| 2. C2×#13133191 | C2 | semidirect |
| 3. #16810959 | C2 | semidirect |
| 4. #16810948 | C2 | semidirect |
| 5. #16810942 | C2 | semidirect |
| 6. #16810859 | C2 | semidirect |
| 7. #16810852 | C2 | semidirect |
| 8. #16810776 | C2 | semidirect |
| 9. #16810770 | C2 | semidirect |
| 10. #16810759 | C2 | semidirect |
| 11. C2×C22⋊C8×C53 | C2 | semidirect |
| 12. C2×#11719945 | C22 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 19. #13133196 | C22 | semidirect |
| 25. #13133191 | C22 | semidirect |
| 29. #13133176 | C22 | semidirect |
| 32. #13133151 | C22 | semidirect |
| 33. #13133149 | C22 | semidirect |
| 34. #13133142 | C22 | semidirect |
| 35. #13133139 | C22 | semidirect |
| 36. #13133139 | C22 | semidirect |
| 37. #13133139 | C22 | semidirect |
| 39. C22×C8×C53 | C22 | semidirect |
| 42. C22⋊C8×C53 | C22 | semidirect |
| 169. C2×C22⋊C8 | D53 | semidirect |
| 170. C53 | #3188 | semidirect |
| 177. C22×C8 | C2×D53 | semidirect |
| 201. C22⋊C8 | C2×D53 | semidirect |