Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×#2241 | C2 | semidirect |
| 2. #71381 | C2 | semidirect |
| 3. #71359 | C2 | semidirect |
| 4. #71313 | C2 | semidirect |
| 5. #71297 | C2 | semidirect |
| 7. #67499 | C2 | semidirect |
| 26. #2241 | D3 | semidirect |
| 219. C3 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2241 | 2 |
| #71381 | 2 |
| #71359 | 2 |
| #71313 | 2 |
| #71297 | 2 |
| #69060 | 2 |
| #67499 | 2 |
| #12527 | 3 |