Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 113 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×#1493 | C2 | semidirect |
| 3. #71826 | C2 | semidirect |
| 4. #70518 | C2 | semidirect |
| 7. C2×#4455 | C2 | semidirect |
| 31. #1493 | D3 | semidirect |
| 311. C3 | #9858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83334 | 2 |
| C3×#1493 | 2 |
| #71826 | 2 |
| #70518 | 2 |
| #70498 | 2 |
| #69735 | 2 |
| C2×#4455 | 2 |
| #9858 | 3 |