Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
392 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. C3×#1383 | C2 | semidirect |
| 5. #67817 | C2 | semidirect |
| 6. #67732 | C2 | semidirect |
| 7. #67720 | C2 | semidirect |
| 20. #4893 | C4 | semidirect |
| 29. #1383 | D3 | semidirect |
| 294. C3 | #12875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4893 | 2 |
| C2×#4514 | 2 |
| #70578 | 2 |
| C3×#1383 | 2 |
| #67817 | 2 |
| #67732 | 2 |
| #67720 | 2 |
| #12875 | 3 |