Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
422 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 115 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×#368 | C2 | semidirect |
| 3. #71399 | C2 | semidirect |
| 4. #70710 | C2 | semidirect |
| 6. C2×#4496 | C2 | semidirect |
| 23. C2×#800 | C4 | semidirect |
| 30. C2×#368 | D3 | semidirect |
| 313. C3 | #13246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#800 | 2 |
| C2×C3×#368 | 2 |
| #71399 | 2 |
| #70710 | 2 |
| #70709 | 2 |
| C2×#4496 | 2 |
| C2×#4495 | 2 |
| #13246 | 3 |