Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. #69045 | C2 | semidirect |
| 3. C3×C4×C32 | C2 | semidirect |
| 4. #67597 | C2 | semidirect |
| 20. C4×C32 | D3 | semidirect |
| 131. C3 | #13721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69062 | 2 |
| #69045 | 2 |
| C3×C4×C32 | 2 |
| #67597 | 2 |
| #67596 | 2 |
| #13721 | 3 |