Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 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×#14524069 | C2 | semidirect |
| 2. C2×M16×D67 | C2 | semidirect |
| 3. #16863908 | C2 | semidirect |
| 4. C2×#14524014 | C2 | semidirect |
| 5. #16863648 | C2 | semidirect |
| 6. #16863641 | C2 | semidirect |
| 7. #16863631 | C2 | semidirect |
| 8. #16863624 | C2 | semidirect |
| 9. #16863439 | C2 | semidirect |
| 10. #16863398 | C2 | semidirect |
| 11. #418×C67 | C2 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 17. C2×#11761613 | C22 | semidirect |
| 19. C2×#11761611 | C22 | semidirect |
| 21. C2×C8×D67 | C22 | semidirect |
| 23. #14524023 | C22 | semidirect |
| 24. #14524023 | C22 | semidirect |
| 25. #14524018 | C22 | semidirect |
| 26. #14524018 | C22 | semidirect |
| 36. #14523976 | C22 | semidirect |
| 37. #14523974 | C22 | semidirect |
| 38. #14523968 | C22 | semidirect |
| 39. #14523965 | C22 | semidirect |
| 43. #102×C67 | C22 | semidirect |
| 44. #102×C67 | C22 | semidirect |
| 67. #11761612 | D4 | semidirect |
| 136. C67⋊C8 | C2×D4 | semidirect |
| 154. C2×D67 | AGL(1,ℤ/8) | semidirect |
| 173. C67 | #3055 | semidirect |
| 183. #418 | D67 | semidirect |
| 216. #102 | C2×D67 | semidirect |
| 217. #102 | C2×D67 | semidirect |