Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
412 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 95 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×#1987 | C2 | semidirect |
| 3. #71790 | C2 | semidirect |
| 5. #70420 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 32. #1987 | D3 | semidirect |
| 356. C3 | #10502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83216 | 2 |
| C3×#1987 | 2 |
| #71790 | 2 |
| #70432 | 2 |
| #70420 | 2 |
| #69492 | 2 |
| #67620 | 2 |
| #10502 | 3 |