Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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×#2227 | C2 | semidirect |
| 3. #71384 | C2 | semidirect |
| 5. #67765 | C2 | semidirect |
| 6. #67565 | C2 | semidirect |
| 28. #2227 | D3 | semidirect |
| 240. C3 | #12398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79742 | 2 |
| C3×#2227 | 2 |
| #71384 | 2 |
| #71372 | 2 |
| #67765 | 2 |
| #67565 | 2 |
| #67556 | 2 |
| #12398 | 3 |