Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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. #16864124 | C2 | semidirect |
| 4. #16863747 | C2 | semidirect |
| 5. #16863704 | C2 | semidirect |
| 8. #16863607 | C2 | semidirect |
| 9. C4×Dic268 | C2 | semidirect |
| 11. C8×Q8×C67 | C2 | semidirect |
| 116. C67 | #3364 | semidirect |
| 125. C8×Q8 | D67 | semidirect |