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×#14524071 | C2 | semidirect |
| 2. C22×#11761613 | C2 | semidirect |
| 3. #16863963 | C2 | semidirect |
| 4. #16863870 | C2 | semidirect |
| 5. #16863610 | C2 | semidirect |
| 6. #16863590 | C2 | semidirect |
| 7. #16863424 | C2 | semidirect |
| 8. #16863390 | C2 | semidirect |
| 9. #418×C67 | C2 | semidirect |
| 13. C2×#11761617 | C22 | semidirect |
| 14. C2×D536 | C22 | semidirect |
| 18. #14524039 | C22 | semidirect |
| 19. #14524030 | C22 | semidirect |
| 23. #14524005 | C22 | semidirect |
| 26. Dic67⋊C8 | C22 | semidirect |
| 27. #14523966 | C22 | semidirect |
| 28. #14523963 | C22 | semidirect |
| 32. #102×C67 | C22 | semidirect |
| 39. C2×D268 | D4 | semidirect |
| 122. C67 | #3041 | semidirect |
| 130. #418 | D67 | semidirect |
| 154. #102 | C2×D67 | semidirect |