Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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×D8×D67 | C2 | semidirect |
| 2. C2×M16×D67 | C2 | semidirect |
| 3. #121×D67 | C2 | semidirect |
| 4. #16863650 | C2 | semidirect |
| 5. #16863649 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863647 | C2 | semidirect |
| 8. #16863646 | C2 | semidirect |
| 9. #106×D67 | C2 | semidirect |
| 10. #102×D67 | C2 | semidirect |
| 11. #469×C67 | C2 | semidirect |
| 15. C2×D536 | C22 | semidirect |
| 16. C2×#11761613 | C22 | semidirect |
| 18. C2×#11761612 | C22 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 20. C2×#11761611 | C22 | semidirect |
| 24. #14524018 | C22 | semidirect |
| 25. #14524017 | C22 | semidirect |
| 28. #14524014 | C22 | semidirect |
| 31. #14523975 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 36. C2×D8×C67 | C22 | semidirect |
| 37. C2×M16×C67 | C22 | semidirect |
| 38. #121×C67 | C22 | semidirect |
| 39. #106×C67 | C22 | semidirect |
| 40. #102×C67 | C22 | semidirect |
| 67. C8×D67 | D4 | semidirect |
| 118. C8×C67 | C2×D4 | semidirect |
| 120. C67⋊C8 | C2×D4 | semidirect |
| 149. D67 | #469 | direct (N × H) |
| 151. C67 | C2×#469 | semidirect |
| 160. #469 | D67 | direct (N × H) |
| 169. C2×D8 | C2×D67 | semidirect |
| 174. C2×M16 | C2×D67 | semidirect |
| 182. #121 | C2×D67 | semidirect |
| 187. #106 | C2×D67 | semidirect |
| 191. #102 | C2×D67 | semidirect |
| 271. C8 | D4×D67 | semidirect |