Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#11761618 | C2 | semidirect |
| 2. C22×#11761617 | C2 | semidirect |
| 4. C2×#14524032 | C2 | semidirect |
| 5. C2×#14524030 | C2 | semidirect |
| 6. #16863777 | C2 | direct (N × H) |
| 7. C2×C8×Dic67 | C2 | semidirect |
| 8. C22×SD16×C67 | C2 | semidirect |
| 12. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761617 | C22 | semidirect |
| 19. #14524032 | C22 | semidirect |
| 21. #14524030 | C22 | semidirect |
| 25. C8×Dic67 | C22 | semidirect |
| 29. C2×SD16×C67 | C22 | semidirect |
| 112. C2×C67 | #495 | semidirect |
| 117. C67 | C2×#495 | semidirect |
| 120. C22×SD16 | D67 | semidirect |
| 135. C2×SD16 | C2×D67 | semidirect |
| 230. C2 | #16863777 | direct (N × H) |