Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 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. #83341 | C2 | semidirect |
| 4. #71835 | C2 | semidirect |
| 6. #70459 | C2 | semidirect |
| 7. #67706 | C2 | semidirect |
| 153. #208 | SD16 | semidirect |
| 370. C3 | #10197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3246 | 2 |
| #83341 | 2 |
| #83317 | 2 |
| #71835 | 2 |
| #71818 | 2 |
| #70459 | 2 |
| #67706 | 2 |
| #10197 | 3 |