Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14524002 | C2 | semidirect |
| 2. #16863717 | C2 | semidirect |
| 3. #16863712 | C2 | semidirect |
| 4. #16863707 | C2 | semidirect |
| 5. #16863436 | C2 | semidirect |
| 6. #16863401 | C2 | semidirect |
| 7. #16863360 | C2 | semidirect |
| 13. #14524002 | C22 | semidirect |
| 14. C2×C4⋊Dic67 | C22 | semidirect |
| 15. C2×C4⋊Dic67 | C22 | semidirect |
| 18. #14523976 | C22 | semidirect |
| 19. #14523974 | C22 | semidirect |
| 20. #14523964 | C22 | semidirect |
| 21. #14523964 | C22 | semidirect |
| 22. C22⋊(C67⋊C8) | C22 | semidirect |
| 23. C22⋊(C67⋊C8) | C22 | semidirect |
| 126. C67 | #3094 | semidirect |