Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
384 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 384 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. C2×C3×#362 | C2 | semidirect |
| 3. #72061 | C2 | semidirect |
| 5. #71427 | C2 | semidirect |
| 7. #67734 | C2 | semidirect |
| 28. C2×#362 | D3 | semidirect |
| 311. C3 | #13403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5192 | 2 |
| C2×C3×#362 | 2 |
| #72061 | 2 |
| #71435 | 2 |
| #71427 | 2 |
| #70719 | 2 |
| #67734 | 2 |
| #13403 | 3 |