Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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×#2155 | C2 | semidirect |
| 3. #71448 | C2 | semidirect |
| 4. #71431 | C2 | semidirect |
| 5. #70711 | C2 | semidirect |
| 6. #70687 | C2 | semidirect |
| 7. #67727 | C2 | semidirect |
| 29. #2155 | D3 | semidirect |
| 62. C2×C3×C16 | D4 | semidirect |
| 175. C2×C16 | D12 | semidirect |
| 356. C3 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79180 | 2 |
| C3×#2155 | 2 |
| #71448 | 2 |
| #71431 | 2 |
| #70711 | 2 |
| #70687 | 2 |
| #67727 | 2 |
| #13395 | 3 |