Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 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×#1566 | C2 | semidirect |
| 4. #70509 | C2 | semidirect |
| 5. #69738 | C2 | semidirect |
| 7. #67711 | C2 | semidirect |
| 32. #1566 | D3 | semidirect |
| 356. C3 | #10460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79059 | 2 |
| C3×#1566 | 2 |
| #70527 | 2 |
| #70509 | 2 |
| #69738 | 2 |
| C2×#4459 | 2 |
| #67711 | 2 |
| #10460 | 3 |