Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14524063 | C2 | semidirect |
| 2. #16863963 | C2 | semidirect |
| 3. #16863879 | C2 | semidirect |
| 4. #16863616 | C2 | semidirect |
| 5. #16863609 | C2 | semidirect |
| 6. #16863594 | C2 | semidirect |
| 7. #16863589 | C2 | semidirect |
| 8. #16863424 | C2 | semidirect |
| 9. #16863398 | C2 | semidirect |
| 10. C2×#14523964 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 14. C2×#11761618 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 16. C2×#11761615 | C22 | semidirect |
| 17. C2×#11761613 | C22 | semidirect |
| 24. Q8×Dic67 | C22 | semidirect |
| 26. D4×Dic67 | C22 | semidirect |
| 31. Dic67⋊C8 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523968 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 73. #41×C67 | D4 | semidirect |
| 155. C67 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 202. #41 | C22⋊D67 | semidirect |