Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#4516 | C2 | semidirect |
| 4. C2×#4514 | C2 | semidirect |
| 5. #70712 | C2 | semidirect |
| 6. C2×#4495 | C2 | semidirect |
| 7. #67720 | C2 | semidirect |
| 27. C2×#365 | D3 | semidirect |
| 57. C3×M32 | D4 | semidirect |
| 160. M32 | D12 | semidirect |
| 336. C3 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4865 | 2 |
| C2×C3×#365 | 2 |
| C2×#4516 | 2 |
| C2×#4514 | 2 |
| #70712 | 2 |
| C2×#4495 | 2 |
| #67720 | 2 |
| #13398 | 3 |