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×#14524071 | C2 | semidirect |
| 2. C2×#14524068 | C2 | semidirect |
| 3. #16863942 | C2 | semidirect |
| 4. C2×#14524005 | C2 | semidirect |
| 5. #16863614 | C2 | semidirect |
| 6. #16863610 | C2 | semidirect |
| 7. #16863600 | C2 | semidirect |
| 8. #16863590 | C2 | semidirect |
| 9. #16863419 | C2 | semidirect |
| 10. #16863395 | C2 | semidirect |
| 11. #417×C67 | C2 | semidirect |
| 22. #14524041 | C22 | semidirect |
| 23. #14524039 | C22 | semidirect |
| 24. #14524032 | C22 | semidirect |
| 25. #14524030 | C22 | semidirect |
| 36. Dic67⋊C8 | C22 | semidirect |
| 37. Dic67⋊C8 | C22 | semidirect |
| 38. #14523966 | C22 | semidirect |
| 39. #14523963 | C22 | semidirect |
| 43. #103×C67 | C22 | semidirect |
| 44. #102×C67 | C22 | semidirect |
| 51. C2×D268 | D4 | semidirect |
| 158. Dic67 | AGL(1,ℤ/8) | semidirect |
| 167. C67 | #3036 | semidirect |
| 178. #417 | D67 | semidirect |
| 209. #103 | C2×D67 | semidirect |
| 211. #102 | C2×D67 | semidirect |