Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 129 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×#1546 | C2 | semidirect |
| 3. #71773 | C2 | semidirect |
| 5. #70740 | C2 | semidirect |
| 6. #70518 | C2 | semidirect |
| 30. #1546 | D3 | semidirect |
| 305. C3 | #9768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5085 | 2 |
| C3×#1546 | 2 |
| #71773 | 2 |
| #70774 | 2 |
| #70740 | 2 |
| #70518 | 2 |
| #70502 | 2 |
| #9768 | 3 |