Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
290 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 290 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×#2240 | C2 | semidirect |
| 2. #71381 | C2 | semidirect |
| 3. #71361 | C2 | semidirect |
| 4. #71288 | C2 | semidirect |
| 6. #69058 | C2 | semidirect |
| 7. #67498 | C2 | semidirect |
| 27. #2240 | D3 | semidirect |
| 211. C3 | #12513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2240 | 2 |
| #71381 | 2 |
| #71361 | 2 |
| #71288 | 2 |
| #71276 | 2 |
| #69058 | 2 |
| #67498 | 2 |
| #12513 | 3 |