Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16864118 | C2 | semidirect |
| 4. #16863774 | C2 | semidirect |
| 5. #16863621 | C2 | semidirect |
| 6. #16863618 | C2 | semidirect |
| 7. #16863600 | C2 | semidirect |
| 8. C8×Dic134 | C2 | semidirect |
| 9. #16863490 | C2 | semidirect |
| 11. C4×Q16×C67 | C2 | semidirect |
| 115. C67 | #3393 | semidirect |
| 125. C4×Q16 | D67 | semidirect |