Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C2×#5069 | C2 | semidirect |
| 5. #71737 | C2 | semidirect |
| 6. #70823 | C2 | semidirect |
| 7. #67751 | C2 | semidirect |
| 331. C3 | #10134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3234 | 2 |
| #83271 | 2 |
| C2×#5069 | 2 |
| #71798 | 2 |
| #71737 | 2 |
| #70823 | 2 |
| #67751 | 2 |
| #10134 | 3 |