Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. C2×Q8×Dic67 | C2 | semidirect |
| 3. #16863724 | C2 | semidirect |
| 5. #16863705 | C2 | semidirect |
| 6. #16863620 | C2 | semidirect |
| 8. Q16×Dic67 | C2 | semidirect |
| 9. #16863481 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 11. #451×C67 | C2 | semidirect |
| 132. C67 | #3108 | semidirect |
| 139. #451 | D67 | semidirect |