Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
846 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×C3×#442 | C2 | semidirect |
| 2. #82307 | C2 | semidirect |
| 3. #78491 | C2 | semidirect |
| 4. #72046 | C2 | semidirect |
| 5. #71617 | C2 | semidirect |
| 6. #70593 | C2 | semidirect |
| 7. #70218 | C2 | semidirect |
| 8. #69841 | C2 | semidirect |
| 32. C2×#442 | D3 | semidirect |
| 327. C3 | #28177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#442 | 2 |
| #82307 | 2 |
| #78491 | 2 |
| #72046 | 2 |
| #71617 | 2 |
| #70593 | 2 |
| #70218 | 2 |
| #69841 | 2 |
| #28177 | 3 |