Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
586 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×C3×#334 | C2 | semidirect |
| 3. #70470 | C2 | semidirect |
| 4. C2×#4483 | C2 | semidirect |
| 5. C2×#4454 | C2 | semidirect |
| 23. C2×#334 | D3 | semidirect |
| 261. C3 | #9665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D24 | 2 |
| C2×C3×#334 | 2 |
| #70470 | 2 |
| C2×#4483 | 2 |
| C2×#4454 | 2 |
| #9665 | 3 |