Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. #16863963 | C2 | semidirect |
| 3. #16863871 | C2 | semidirect |
| 4. #16863609 | C2 | semidirect |
| 5. #16863589 | C2 | semidirect |
| 6. #16863422 | C2 | semidirect |
| 7. #16863401 | C2 | semidirect |
| 8. #16863393 | C2 | semidirect |
| 9. C22×D8×C67 | C2 | semidirect |
| 12. C2×#11761616 | C22 | semidirect |
| 13. C2×#11761613 | C22 | semidirect |
| 15. #14524039 | C22 | semidirect |
| 16. #14524030 | C22 | semidirect |
| 20. D4×Dic67 | C22 | semidirect |
| 24. Dic67⋊C8 | C22 | semidirect |
| 25. #14523968 | C22 | semidirect |
| 26. #14523965 | C22 | semidirect |
| 27. #14523964 | C22 | semidirect |
| 60. C2×D4×C67 | D4 | semidirect |
| 122. C67 | #3041 | semidirect |
| 124. C22×D8 | D67 | semidirect |
| 168. C2×D4 | C22⋊D67 | semidirect |