Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
212 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 77 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. #70906 | C2 | semidirect |
| 4. #67764 | C2 | semidirect |
| 6. #67513 | C2 | semidirect |
| 7. #67511 | C2 | semidirect |
| 88. C3×C16 | M16 | semidirect |
| 153. C16 | #208 | semidirect |
| 200. C3 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2175 | 2 |
| #70906 | 2 |
| #70882 | 2 |
| #67764 | 2 |
| #67762 | 2 |
| #67513 | 2 |
| #67511 | 2 |
| #12087 | 3 |