Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
426 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. C3×#1286 | C2 | semidirect |
| 5. #67746 | C2 | semidirect |
| 6. #67715 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 30. #1286 | D3 | semidirect |
| 322. C3 | #8770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #74160 | 2 |
| #70783 | 2 |
| #70527 | 2 |
| C3×#1286 | 2 |
| #67746 | 2 |
| #67715 | 2 |
| #67631 | 2 |
| #8770 | 3 |