Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
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. #16863907 | C2 | semidirect |
| 2. C2×#14524017 | C2 | semidirect |
| 3. #16863732 | C2 | semidirect |
| 4. #16863721 | C2 | semidirect |
| 5. #16863715 | C2 | semidirect |
| 6. #16863632 | C2 | semidirect |
| 7. #16863625 | C2 | semidirect |
| 8. #16863549 | C2 | semidirect |
| 9. #16863543 | C2 | semidirect |
| 10. #16863532 | C2 | semidirect |
| 11. C2×C22⋊C8×C67 | C2 | semidirect |
| 12. C2×#11761628 | C22 | semidirect |
| 15. C2×#11761617 | C22 | semidirect |
| 16. C2×D536 | C22 | semidirect |
| 19. #14524022 | C22 | semidirect |
| 25. #14524017 | C22 | semidirect |
| 29. #14524002 | C22 | semidirect |
| 32. #14523977 | C22 | semidirect |
| 33. #14523975 | C22 | semidirect |
| 34. #14523968 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 36. #14523965 | C22 | semidirect |
| 37. #14523965 | C22 | semidirect |
| 39. C22×C8×C67 | C22 | semidirect |
| 42. C22⋊C8×C67 | C22 | semidirect |
| 159. C67 | #3188 | semidirect |
| 170. C2×C22⋊C8 | D67 | semidirect |
| 177. C22×C8 | C2×D67 | semidirect |
| 201. C22⋊C8 | C2×D67 | semidirect |