Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
506 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 506 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 |
|---|---|---|
| 2. #83317 | C2 | semidirect |
| 3. C2×#5055 | C2 | semidirect |
| 4. #71798 | C2 | semidirect |
| 5. #71720 | C2 | semidirect |
| 6. #70822 | C2 | semidirect |
| 7. #67751 | C2 | semidirect |
| 360. C3 | #10136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3213 | 2 |
| #83317 | 2 |
| C2×#5055 | 2 |
| #71798 | 2 |
| #71720 | 2 |
| #70822 | 2 |
| #67751 | 2 |
| #10136 | 3 |