Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 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. #83128 | C2 | semidirect |
| 3. C3×#1532 | C2 | semidirect |
| 4. #70828 | C2 | semidirect |
| 5. C2×#4464 | C2 | semidirect |
| 6. #67751 | C2 | semidirect |
| 7. #67661 | C2 | semidirect |
| 38. #1532 | D3 | semidirect |
| 417. C3 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83144 | 2 |
| #83128 | 2 |
| C3×#1532 | 2 |
| #70828 | 2 |
| C2×#4464 | 2 |
| #67751 | 2 |
| #67661 | 2 |
| #9265 | 3 |