Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 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. #16864001 | C2 | semidirect |
| 2. #16863786 | C2 | semidirect |
| 3. #16863770 | C2 | semidirect |
| 4. #16863764 | C2 | semidirect |
| 5. #16863750 | C2 | semidirect |
| 6. #16863608 | C2 | semidirect |
| 7. #16863598 | C2 | semidirect |
| 8. #16863541 | C2 | semidirect |
| 9. #16863535 | C2 | semidirect |
| 10. #16863457 | C2 | semidirect |
| 11. #536×C67 | C2 | semidirect |
| 121. C67 | #3221 | semidirect |
| 123. #536 | D67 | semidirect |