Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#14524063 | C2 | semidirect |
| 3. #16863876 | C2 | semidirect |
| 4. #16863615 | C2 | semidirect |
| 5. #16863608 | C2 | semidirect |
| 6. #16863593 | C2 | semidirect |
| 7. #16863588 | C2 | semidirect |
| 8. #16863423 | C2 | semidirect |
| 9. #16863397 | C2 | semidirect |
| 10. C2×#14523964 | C2 | semidirect |
| 11. #535×C67 | C2 | semidirect |
| 15. C2×#11761618 | C22 | semidirect |
| 17. C2×#11761616 | C22 | semidirect |
| 18. C2×#11761615 | C22 | semidirect |
| 20. C2×#11761613 | C22 | semidirect |
| 23. C4×Dic134 | C22 | semidirect |
| 24. C4×D268 | C22 | semidirect |
| 29. C4⋊(C67⋊C8) | C22 | semidirect |
| 30. C4⋊(C67⋊C8) | C22 | semidirect |
| 31. #14523967 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 44. #11761628 | D4 | semidirect |
| 155. C67 | #3045 | semidirect |
| 158. #535 | D67 | semidirect |