Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
180 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 57 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. #69321 | C2 | semidirect |
| 3. C3×#1416 | C2 | semidirect |
| 4. #67826 | C2 | semidirect |
| 6. Dic3×C32 | C2 | semidirect |
| 23. #1416 | D3 | semidirect |
| 166. C3 | #13721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #71500 | 2 |
| #69321 | 2 |
| C3×#1416 | 2 |
| #67826 | 2 |
| #67596 | 2 |
| Dic3×C32 | 2 |
| #67577 | 2 |
| #13721 | 3 |