Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
590 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. C3×#3227 | C2 | semidirect |
| 3. #83260 | C2 | semidirect |
| 4. #71811 | C2 | semidirect |
| 5. #71775 | C2 | semidirect |
| 6. #70756 | C2 | semidirect |
| 7. #67746 | C2 | semidirect |
| 32. #3227 | D3 | semidirect |
| 419. C3 | #10241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3227 | 2 |
| #83297 | 2 |
| #83260 | 2 |
| #71811 | 2 |
| #71775 | 2 |
| #70756 | 2 |
| #67746 | 2 |
| #10241 | 3 |