Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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. #16863930 | C2 | semidirect |
| 2. #16863783 | C2 | semidirect |
| 3. #16863760 | C2 | semidirect |
| 4. #16863593 | C2 | semidirect |
| 5. #16863588 | C2 | semidirect |
| 6. #16863547 | C2 | semidirect |
| 7. #16863530 | C2 | semidirect |
| 8. #16863453 | C2 | semidirect |
| 9. C2×#127×C67 | C2 | semidirect |
| 10. C2×#11761616 | C22 | semidirect |
| 11. C2×#11761613 | C22 | semidirect |
| 13. #14524035 | C22 | semidirect |
| 14. #14524031 | C22 | semidirect |
| 18. C4×Dic134 | C22 | semidirect |
| 19. C4×D268 | C22 | semidirect |
| 22. C4⋊(C67⋊C8) | C22 | semidirect |
| 23. #14523964 | C22 | semidirect |
| 24. #14523964 | C22 | semidirect |
| 26. #14523954 | C22 | semidirect |
| 128. C67 | #3217 | semidirect |
| 129. C2×#127 | D67 | semidirect |