Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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×#2155 | C2 | semidirect |
| 3. #71448 | C2 | semidirect |
| 4. #71432 | C2 | semidirect |
| 5. #70665 | C2 | semidirect |
| 6. #70651 | C2 | semidirect |
| 7. #67728 | C2 | semidirect |
| 29. #2155 | D3 | semidirect |
| 342. C3 | #13406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79256 | 2 |
| C3×#2155 | 2 |
| #71448 | 2 |
| #71432 | 2 |
| #70665 | 2 |
| #70651 | 2 |
| #67728 | 2 |
| #13406 | 3 |