Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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. #70710 | C2 | semidirect |
| 5. C2×#4496 | C2 | semidirect |
| 6. C3×#1385 | C2 | semidirect |
| 7. #67813 | C2 | semidirect |
| 22. C2×Dic24 | C4 | semidirect |
| 23. C2×#800 | C4 | semidirect |
| 33. #1385 | D3 | semidirect |
| 325. C3 | #13035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4909 | 2 |
| #79249 | 2 |
| #70710 | 2 |
| #70690 | 2 |
| C2×#4496 | 2 |
| C3×#1385 | 2 |
| #67813 | 2 |
| #13035 | 3 |