Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1801 | C2 | semidirect |
| 3. #71621 | C2 | semidirect |
| 6. #70494 | C2 | semidirect |
| 7. #67714 | C2 | semidirect |
| 27. #1801 | 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×#5027 | 2 |
| C3×#1801 | 2 |
| #71621 | 2 |
| #70502 | 2 |
| #70494 | 2 |
| #67714 | 2 |
| #10442 | 3 |