Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14524066 | C2 | semidirect |
| 2. C22×D536 | C2 | semidirect |
| 3. #16864037 | C2 | semidirect |
| 4. #16863781 | C2 | semidirect |
| 5. #16863633 | C2 | semidirect |
| 6. #16863614 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. #16863544 | C2 | semidirect |
| 9. #16863478 | C2 | semidirect |
| 10. C8×C22⋊D67 | C2 | semidirect |
| 11. #467×C67 | C2 | semidirect |
| 12. C2×#11761629 | C22 | semidirect |
| 15. C2×#11761615 | C22 | semidirect |
| 16. C2×#11761615 | C22 | semidirect |
| 21. C2×C8×D67 | C22 | semidirect |
| 22. #14524032 | C22 | semidirect |
| 25. #14524018 | C22 | semidirect |
| 27. #14524005 | C22 | semidirect |
| 30. Dic67⋊C8 | C22 | semidirect |
| 31. #14523963 | C22 | semidirect |
| 32. #14523963 | C22 | semidirect |
| 34. (C2×D67)⋊C8 | C22 | semidirect |
| 35. C8×Dic67 | C22 | semidirect |
| 36. C2×Q16×C67 | C22 | semidirect |
| 39. #107×C67 | C22 | semidirect |
| 40. #103×C67 | C22 | semidirect |
| 59. D536 | D4 | semidirect |
| 116. C22×C67 | #135 | semidirect |
| 144. C67 | #3280 | semidirect |
| 149. #467 | D67 | semidirect |
| 159. C2×Q16 | C2×D67 | semidirect |
| 177. #107 | C2×D67 | semidirect |
| 179. #103 | C2×D67 | semidirect |
| 270. C22 | #14524066 | semidirect |