Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Dic134 | C2 | semidirect |
| 3. #16863727 | C2 | semidirect |
| 5. #16863704 | C2 | semidirect |
| 6. #16863619 | C2 | semidirect |
| 7. #16863554 | C2 | semidirect |
| 9. C4×Dic268 | C2 | semidirect |
| 10. C4×#11761617 | C2 | semidirect |
| 11. #431×C67 | C2 | semidirect |
| 132. C67 | #3108 | semidirect |
| 143. #431 | D67 | semidirect |