Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
252 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #71291 | C2 | semidirect |
| 3. #69277 | C2 | semidirect |
| 4. #68577 | C2 | semidirect |
| 5. C3×#1361 | C2 | semidirect |
| 6. #67561 | C2 | semidirect |
| 7. #67470 | C2 | semidirect |
| 30. #1361 | D3 | semidirect |
| 96. C3⋊C16 | D8 | semidirect |
| 133. D12 | SD32 | semidirect |
| 229. C3 | #12432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #71291 | 2 |
| #71282 | 2 |
| #69277 | 2 |
| #68577 | 2 |
| C3×#1361 | 2 |
| #67561 | 2 |
| #67470 | 2 |
| #12432 | 3 |