Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #74159 | C2 | semidirect |
| 4. #70766 | C2 | semidirect |
| 6. C3×#1286 | C2 | semidirect |
| 7. #67715 | C2 | semidirect |
| 20. #4849 | C4 | semidirect |
| 21. #4848 | C4 | semidirect |
| 36. #1286 | D3 | semidirect |
| 388. C3 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79067 | 2 |
| #74159 | 2 |
| #70789 | 2 |
| #70766 | 2 |
| #69545 | 2 |
| C3×#1286 | 2 |
| #67715 | 2 |
| #9182 | 3 |