Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#5069 | C2 | semidirect |
| 4. C3×#1470 | C2 | semidirect |
| 5. #70822 | C2 | semidirect |
| 7. #67742 | C2 | semidirect |
| 37. #1470 | D3 | semidirect |
| 331. C3 | #10134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83019 | 2 |
| C2×#5069 | 2 |
| #79269 | 2 |
| C3×#1470 | 2 |
| #70822 | 2 |
| #70806 | 2 |
| #67742 | 2 |
| #10134 | 3 |