Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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. #83280 | C2 | semidirect |
| 3. C3×#1557 | C2 | semidirect |
| 4. #70827 | C2 | semidirect |
| 5. #70496 | C2 | semidirect |
| 6. #67756 | C2 | semidirect |
| 7. #67716 | C2 | semidirect |
| 32. #1557 | D3 | semidirect |
| 352. C3 | #9529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83300 | 2 |
| #83280 | 2 |
| C3×#1557 | 2 |
| #70827 | 2 |
| #70496 | 2 |
| #67756 | 2 |
| #67716 | 2 |
| #9529 | 3 |