Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. #83130 | C2 | semidirect |
| 3. C3×#1524 | C2 | semidirect |
| 4. #69855 | C2 | semidirect |
| 5. #69837 | C2 | semidirect |
| 6. #67668 | C2 | semidirect |
| 7. #67662 | C2 | semidirect |
| 39. #1524 | D3 | semidirect |
| 447. C3 | #9052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83141 | 2 |
| #83130 | 2 |
| C3×#1524 | 2 |
| #69855 | 2 |
| #69837 | 2 |
| #67668 | 2 |
| #67662 | 2 |
| #9052 | 3 |