Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #70767 | C2 | semidirect |
| 4. #70528 | C2 | semidirect |
| 6. #70422 | C2 | semidirect |
| 7. C3×#1301 | C2 | semidirect |
| 32. #1301 | D3 | semidirect |
| 340. C3 | #10442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4848 | 2 |
| #70774 | 2 |
| #70767 | 2 |
| #70528 | 2 |
| #70502 | 2 |
| #70422 | 2 |
| C3×#1301 | 2 |
| #10442 | 3 |