Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 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×#2159 | C2 | semidirect |
| 3. C2×#4516 | C2 | semidirect |
| 4. C2×#4515 | C2 | semidirect |
| 5. #70646 | C2 | semidirect |
| 6. C2×#4491 | C2 | semidirect |
| 7. #67724 | C2 | semidirect |
| 29. #2159 | D3 | semidirect |
| 60. C3×M32 | D4 | semidirect |
| 169. M32 | D12 | semidirect |
| 359. C3 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79183 | 2 |
| C3×#2159 | 2 |
| C2×#4516 | 2 |
| C2×#4515 | 2 |
| #70646 | 2 |
| C2×#4491 | 2 |
| #67724 | 2 |
| #13387 | 3 |