Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16864119 | C2 | semidirect |
| 3. #16863794 | C2 | semidirect |
| 4. #16863735 | C2 | semidirect |
| 5. #16863719 | C2 | semidirect |
| 6. #16863691 | C2 | semidirect |
| 7. #16863676 | C2 | semidirect |
| 8. #16863622 | C2 | semidirect |
| 9. C8×D268 | C2 | semidirect |
| 10. #16863431 | C2 | semidirect |
| 11. C4×SD16×C67 | C2 | semidirect |
| 121. C67 | #3340 | semidirect |
| 130. C4×SD16 | D67 | semidirect |