Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 2. C2×C3×#365 | C2 | semidirect |
| 3. #71450 | C2 | semidirect |
| 4. #71438 | C2 | semidirect |
| 5. #70719 | C2 | semidirect |
| 6. #70687 | C2 | semidirect |
| 7. #67721 | C2 | semidirect |
| 29. C2×#365 | D3 | semidirect |
| 61. C3×M32 | D4 | semidirect |
| 173. M32 | D12 | semidirect |
| 350. C3 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79120 | 2 |
| C2×C3×#365 | 2 |
| #71450 | 2 |
| #71438 | 2 |
| #70719 | 2 |
| #70687 | 2 |
| #67721 | 2 |
| #13400 | 3 |