Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. C3×#1565 | C2 | semidirect |
| 3. #70456 | C2 | semidirect |
| 5. #69879 | C2 | semidirect |
| 7. #67746 | C2 | semidirect |
| 34. #1565 | D3 | semidirect |
| 120. C3×M16 | SD16 | semidirect |
| 255. M16 | #204 | semidirect |
| 366. C3 | #10501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79312 | 2 |
| C3×#1565 | 2 |
| #70456 | 2 |
| #70432 | 2 |
| #69879 | 2 |
| #69867 | 2 |
| #67746 | 2 |
| #10501 | 3 |