Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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×#1744 | C2 | semidirect |
| 3. C2×#4456 | C2 | semidirect |
| 5. #69392 | C2 | semidirect |
| 24. #1744 | D3 | semidirect |
| 296. C3 | #9645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#875 | 2 |
| C3×#1744 | 2 |
| C2×#4456 | 2 |
| C2×#4459 | 2 |
| #69392 | 2 |
| #9645 | 3 |