Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16863932 | C2 | semidirect |
| 2. #16863797 | C2 | semidirect |
| 3. #16863781 | C2 | semidirect |
| 4. #16863752 | C2 | semidirect |
| 6. #16863627 | C2 | semidirect |
| 7. Q16×Dic67 | C2 | semidirect |
| 8. #16863481 | C2 | semidirect |
| 9. #16863478 | C2 | semidirect |
| 10. C2×C8×Dic67 | C2 | semidirect |
| 11. #467×C67 | C2 | semidirect |
| 119. C67 | #3168 | semidirect |
| 124. #467 | D67 | semidirect |