Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1567 | C2 | semidirect |
| 3. #70528 | C2 | semidirect |
| 5. C2×#4456 | C2 | semidirect |
| 7. #67711 | C2 | semidirect |
| 32. #1567 | D3 | semidirect |
| 370. C3 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79067 | 2 |
| C3×#1567 | 2 |
| #70528 | 2 |
| #70503 | 2 |
| C2×#4456 | 2 |
| #69735 | 2 |
| #67711 | 2 |
| #10458 | 3 |