Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2162 | C2 | semidirect |
| 3. #69745 | C2 | semidirect |
| 4. #67557 | C2 | semidirect |
| 23. #2162 | D3 | semidirect |
| 237. C3 | #11633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78458 | 2 |
| C3×#2162 | 2 |
| #69745 | 2 |
| #67557 | 2 |
| #11633 | 3 |