Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14524062 | C2 | semidirect |
| 2. #16864040 | C2 | semidirect |
| 3. #16863779 | C2 | semidirect |
| 4. #16863637 | C2 | semidirect |
| 5. #16863629 | C2 | semidirect |
| 6. #16863609 | C2 | semidirect |
| 7. #16863547 | C2 | semidirect |
| 8. #16863538 | C2 | semidirect |
| 9. D8×Dic67 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. C22×D8×C67 | C2 | semidirect |
| 12. C2×#11761627 | C22 | semidirect |
| 14. C2×Dic268 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 17. C2×C8×D67 | C22 | semidirect |
| 18. #14524030 | C22 | semidirect |
| 22. #14524014 | C22 | semidirect |
| 24. D4×Dic67 | C22 | semidirect |
| 27. #14523977 | C22 | semidirect |
| 28. Dic67⋊C8 | C22 | semidirect |
| 29. #14523968 | C22 | semidirect |
| 30. #14523964 | C22 | semidirect |
| 31. #14523964 | C22 | semidirect |
| 33. (C2×D67)⋊C8 | C22 | semidirect |
| 34. C8×Dic67 | C22 | semidirect |
| 76. D8×C67 | D4 | semidirect |
| 123. C22×C67 | #135 | semidirect |
| 144. C67 | #3280 | semidirect |
| 146. C22×D8 | D67 | semidirect |
| 206. D8 | C22⋊D67 | semidirect |
| 270. C22 | #14524062 | semidirect |