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 |
| 4. C2×#4496 | C2 | semidirect |
| 6. C3×#1388 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 21. #4909 | C4 | semidirect |
| 34. #1388 | D3 | semidirect |
| 327. C3 | #13031 | 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 |
| C2×#4496 | 2 |
| #70687 | 2 |
| C3×#1388 | 2 |
| #67814 | 2 |
| #13031 | 3 |