Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #16863406 | C2 | semidirect |
| 4. #16863404 | C2 | semidirect |
| 6. #16863156 | C2 | semidirect |
| 7. #339×C67 | C2 | semidirect |
| 12. #14524031 | C4 | semidirect |
| 30. C2×Dic134 | C2×C4 | semidirect |
| 56. C42×C67 | C2×C4 | semidirect |
| 108. C67 | #1885 | semidirect |
| 115. #339 | D67 | semidirect |
| 164. C42 | C4×D67 | semidirect |