Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
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×#14524065 | C2 | semidirect |
| 2. C2×D8×D67 | C2 | semidirect |
| 3. #16864043 | C2 | semidirect |
| 4. #16863779 | C2 | semidirect |
| 5. #16863638 | C2 | semidirect |
| 6. #16863610 | C2 | semidirect |
| 7. #16863548 | C2 | semidirect |
| 8. #16863539 | C2 | semidirect |
| 9. #16863478 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. #466×C67 | C2 | semidirect |
| 12. C2×#11761628 | C22 | semidirect |
| 15. C2×Dic268 | C22 | semidirect |
| 16. C2×#11761617 | C22 | semidirect |
| 17. C2×#11761616 | C22 | semidirect |
| 22. #14524030 | C22 | semidirect |
| 27. #14524005 | C22 | semidirect |
| 30. Dic67⋊C8 | C22 | semidirect |
| 31. #14523966 | C22 | semidirect |
| 32. #14523963 | C22 | semidirect |
| 33. C22⋊(C67⋊C8) | C22 | semidirect |
| 35. C8×Dic67 | C22 | semidirect |
| 37. C22×C8×C67 | C22 | semidirect |
| 38. #121×C67 | C22 | semidirect |
| 39. #107×C67 | C22 | semidirect |
| 40. #102×C67 | C22 | semidirect |
| 57. D536 | D4 | semidirect |
| 127. C2×D67 | #135 | semidirect |
| 144. C67 | #3280 | semidirect |
| 150. #466 | D67 | semidirect |
| 167. C22×C8 | C2×D67 | semidirect |
| 172. #121 | C2×D67 | semidirect |
| 177. #107 | C2×D67 | semidirect |
| 181. #102 | C2×D67 | semidirect |