Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
504 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 143 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. C3×#2241 | C2 | semidirect |
| 4. #71385 | C2 | semidirect |
| 5. #71312 | C2 | semidirect |
| 7. #69209 | C2 | semidirect |
| 8. #69065 | C2 | semidirect |
| 41. #2241 | D3 | semidirect |
| 310. C3 | #33749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81934 | 2 |
| #81792 | 2 |
| C3×#2241 | 2 |
| #71385 | 2 |
| #71312 | 2 |
| #69229 | 2 |
| #69209 | 2 |
| #69065 | 2 |
| C4×#798 | 2 |
| #33749 | 3 |