Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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. #71425 | C2 | semidirect |
| 5. #69882 | C2 | semidirect |
| 6. C3×#1378 | C2 | semidirect |
| 7. #67815 | C2 | semidirect |
| 30. #1378 | D3 | semidirect |
| 269. C3 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #71438 | 2 |
| C2×#4515 | 2 |
| #71425 | 2 |
| #69898 | 2 |
| #69882 | 2 |
| C3×#1378 | 2 |
| #67815 | 2 |
| #13126 | 3 |