Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14524073 | C2 | semidirect |
| 2. C22×#11761616 | C2 | semidirect |
| 3. #16863967 | C2 | semidirect |
| 4. #16863558 | C2 | semidirect |
| 5. #16863547 | C2 | semidirect |
| 6. #16863401 | C2 | semidirect |
| 7. #16863392 | C2 | semidirect |
| 8. #16863363 | C2 | semidirect |
| 10. C22×Dic134 | C22 | semidirect |
| 12. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761616 | C22 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 16. C2×#11761612 | C22 | semidirect |
| 17. C22×C67⋊C8 | C22 | semidirect |
| 21. #14524022 | C22 | semidirect |
| 22. #14524002 | C22 | semidirect |
| 23. #14523967 | C22 | semidirect |
| 24. #14523964 | C22 | semidirect |
| 25. #14523964 | C22 | semidirect |
| 26. C22⋊(C67⋊C8) | C22 | semidirect |
| 147. C67 | #3009 | semidirect |