Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
354 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 83 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. #69073 | C2 | semidirect |
| 3. D3×#334 | C2 | semidirect |
| 4. C3×#1333 | C2 | semidirect |
| 5. #67762 | C2 | semidirect |
| 6. #67516 | C2 | semidirect |
| 7. #67465 | C2 | semidirect |
| 34. #1333 | D3 | semidirect |
| 312. C3 | #11654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79598 | 2 |
| #69073 | 2 |
| D3×#334 | 2 |
| C3×#1333 | 2 |
| #67762 | 2 |
| #67516 | 2 |
| #67465 | 2 |
| #11654 | 3 |