Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. #71442 | C2 | semidirect |
| 3. #71431 | C2 | semidirect |
| 4. #70711 | C2 | semidirect |
| 5. #70690 | C2 | semidirect |
| 6. #70650 | C2 | semidirect |
| 7. C3×#1389 | C2 | semidirect |
| 34. #1389 | D3 | semidirect |
| 72. C2×C3⋊C16 | D4 | 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 |
| #71442 | 2 |
| #71431 | 2 |
| #70711 | 2 |
| #70690 | 2 |
| #70650 | 2 |
| C3×#1389 | 2 |
| #13395 | 3 |