Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70823 | C2 | semidirect |
| 4. #70822 | C2 | semidirect |
| 6. C3×#1291 | C2 | semidirect |
| 7. #67670 | C2 | semidirect |
| 32. #1291 | D3 | semidirect |
| 295. C3 | #9421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79337 | 2 |
| #78538 | 2 |
| #70823 | 2 |
| #70822 | 2 |
| #70811 | 2 |
| C3×#1291 | 2 |
| #67670 | 2 |
| #9421 | 3 |