Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14524018 | C2 | semidirect |
| 2. #121×D67 | C2 | semidirect |
| 3. #16863716 | C2 | semidirect |
| 4. #16863714 | C2 | semidirect |
| 5. #16863650 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863532 | C2 | semidirect |
| 8. #16863531 | C2 | semidirect |
| 9. #16863529 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #481×C67 | C2 | semidirect |
| 13. C22×D268 | C22 | semidirect |
| 15. C2×D4×D67 | C22 | semidirect |
| 17. C2×D536 | C22 | semidirect |
| 18. C2×#11761613 | C22 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 23. #14524018 | C22 | semidirect |
| 24. #14524018 | C22 | semidirect |
| 28. #14524014 | C22 | semidirect |
| 29. C4⋊C4×D67 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523963 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 36. C22⋊(C67⋊C8) | C22 | semidirect |
| 37. (C2×D67)⋊C8 | C22 | semidirect |
| 39. C2×C4⋊C4×C67 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 42. C22⋊C8×C67 | C22 | semidirect |
| 169. C67 | #3192 | semidirect |
| 174. #481 | D67 | semidirect |
| 200. C2×C4⋊C4 | C2×D67 | semidirect |
| 204. #106 | C2×D67 | semidirect |
| 208. #102 | C2×D67 | semidirect |
| 211. C22⋊C8 | C2×D67 | semidirect |