Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. Q8×D268 | C2 | semidirect |
| 2. #16863755 | C2 | semidirect |
| 3. #16863746 | C2 | semidirect |
| 4. #16863691 | C2 | semidirect |
| 5. #16863676 | C2 | semidirect |
| 7. #16863598 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 9. #16863494 | C2 | semidirect |
| 11. #556×C67 | C2 | semidirect |
| 123. C67 | #3367 | semidirect |
| 124. #556 | D67 | semidirect |