Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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×#368 | C2 | semidirect |
| 5. #70683 | C2 | semidirect |
| 6. #67807 | C2 | semidirect |
| 7. #67735 | C2 | semidirect |
| 23. #4508 | C4 | semidirect |
| 27. C2×#368 | D3 | semidirect |
| 269. C3 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79252 | 2 |
| C2×C3×#368 | 2 |
| C2×#4508 | 2 |
| #70719 | 2 |
| #70683 | 2 |
| #67807 | 2 |
| #67735 | 2 |
| #12927 | 3 |