Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 89 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×#2140 | C2 | semidirect |
| 3. #72033 | C2 | semidirect |
| 4. #71437 | C2 | semidirect |
| 5. #71427 | C2 | semidirect |
| 6. #70664 | C2 | semidirect |
| 7. #67727 | C2 | semidirect |
| 29. #2140 | D3 | semidirect |
| 322. C3 | #13404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5160 | 2 |
| C3×#2140 | 2 |
| #72033 | 2 |
| #71437 | 2 |
| #71427 | 2 |
| #70664 | 2 |
| #67727 | 2 |
| #13404 | 3 |