Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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. #71384 | C2 | semidirect |
| 3. #69289 | C2 | semidirect |
| 4. #68578 | C2 | semidirect |
| 5. C3×#1364 | C2 | semidirect |
| 6. #67556 | C2 | semidirect |
| 7. #67471 | C2 | semidirect |
| 30. #1364 | D3 | semidirect |
| 261. C3 | #12392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81946 | 2 |
| #71384 | 2 |
| #69289 | 2 |
| #68578 | 2 |
| C3×#1364 | 2 |
| #67556 | 2 |
| #67471 | 2 |
| #12392 | 3 |