Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
454 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 454 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. #16863930 | C2 | semidirect |
| 2. #16863731 | C2 | semidirect |
| 3. #16863714 | C2 | semidirect |
| 4. #16863696 | C2 | semidirect |
| 5. #16863611 | C2 | semidirect |
| 6. #16863547 | C2 | semidirect |
| 8. C4×#11761616 | C2 | semidirect |
| 9. C4×#11761613 | C2 | semidirect |
| 10. #16863449 | C2 | semidirect |
| 11. C2×C4×D4×C67 | C2 | semidirect |
| 15. #14524035 | C22 | semidirect |
| 16. #14524031 | C22 | semidirect |
| 20. C4×Dic134 | C22 | semidirect |
| 21. C4×D268 | C22 | semidirect |
| 24. #14523976 | C22 | semidirect |
| 25. #14523974 | C22 | semidirect |
| 26. C4⋊(C67⋊C8) | C22 | semidirect |
| 27. #14523966 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 33. C4×C67⋊C8 | C22 | semidirect |
| 141. C67 | #3105 | semidirect |
| 143. C2×C4×D4 | D67 | semidirect |