Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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. #16863710 | C2 | semidirect |
| 4. #16863707 | C2 | semidirect |
| 5. #16863689 | C2 | semidirect |
| 6. #16863594 | C2 | semidirect |
| 7. #16863535 | C2 | semidirect |
| 8. #16863499 | C2 | semidirect |
| 9. #16863497 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 11. #448×C67 | C2 | semidirect |
| 87. Q8×C67 | #41 | semidirect |
| 141. C67 | #3112 | semidirect |
| 149. #448 | D67 | semidirect |
| 229. Q8 | #11761627 | semidirect |