Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#13133245 | C2 | semidirect |
| 2. #16811201 | C2 | semidirect |
| 3. #16811187 | C2 | semidirect |
| 4. #16810876 | C2 | semidirect |
| 5. #16810869 | C2 | semidirect |
| 6. #16810859 | C2 | semidirect |
| 7. #16810852 | C2 | semidirect |
| 8. #16810665 | C2 | semidirect |
| 9. #16810620 | C2 | semidirect |
| 10. C2×#13133139 | C2 | semidirect |
| 11. C2×#131×C53 | C2 | semidirect |
| 19. #13133196 | C22 | semidirect |
| 23. #13133191 | C22 | semidirect |
| 29. #13133151 | C22 | semidirect |
| 30. #13133149 | C22 | semidirect |
| 31. #13133142 | C22 | semidirect |
| 32. #13133142 | C22 | semidirect |
| 35. #13133139 | C22 | semidirect |
| 36. #13133139 | C22 | semidirect |
| 40. C2×M16×C53 | C22 | semidirect |
| 42. C22×C8×C53 | C22 | semidirect |
| 66. M16×C53 | D4 | semidirect |
| 153. C2×#131 | D53 | semidirect |
| 163. C53 | #3062 | semidirect |
| 172. C2×M16 | C2×D53 | semidirect |
| 174. C22×C8 | C2×D53 | semidirect |
| 220. M16 | C22⋊D53 | semidirect |