Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16864116 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863721 | C2 | semidirect |
| 5. #16863682 | C2 | semidirect |
| 6. #16863625 | C2 | semidirect |
| 7. #16863597 | C2 | semidirect |
| 8. #16863560 | C2 | semidirect |
| 9. C4×Dic268 | C2 | semidirect |
| 10. #16863393 | C2 | semidirect |
| 11. C8×D4×C67 | C2 | semidirect |
| 128. C67 | #3304 | semidirect |
| 138. C8×D4 | D67 | semidirect |