Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524069 | C2 | semidirect |
| 2. C22×#11761613 | C2 | semidirect |
| 3. #16863965 | C2 | semidirect |
| 4. #16863611 | C2 | semidirect |
| 5. #16863591 | C2 | semidirect |
| 6. #16863423 | C2 | semidirect |
| 7. #16863400 | C2 | semidirect |
| 8. #16863390 | C2 | semidirect |
| 9. #518×C67 | C2 | semidirect |
| 13. C2×#11761616 | C22 | semidirect |
| 16. C2×#11761613 | C22 | semidirect |
| 19. #14524040 | C22 | semidirect |
| 20. #14524031 | C22 | semidirect |
| 23. C4⋊(C67⋊C8) | C22 | semidirect |
| 24. #14523966 | C22 | semidirect |
| 25. #14523963 | C22 | semidirect |
| 26. #14523963 | C22 | semidirect |
| 29. C4×D4×C67 | C22 | semidirect |
| 56. C2×D4×C67 | D4 | semidirect |
| 122. C67 | #3041 | semidirect |
| 126. #518 | D67 | semidirect |
| 147. C4×D4 | C2×D67 | semidirect |
| 169. C2×D4 | D268 | semidirect |