Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
514 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 129 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. C3×#1492 | C2 | semidirect |
| 3. #71802 | C2 | semidirect |
| 4. #70518 | C2 | semidirect |
| 5. #70498 | C2 | semidirect |
| 6. #69735 | C2 | semidirect |
| 7. C2×#4454 | C2 | semidirect |
| 33. #1492 | D3 | semidirect |
| 342. C3 | #9862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83285 | 2 |
| C3×#1492 | 2 |
| #71802 | 2 |
| #70518 | 2 |
| #70498 | 2 |
| #69735 | 2 |
| C2×#4454 | 2 |
| #9862 | 3 |