Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
322 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 113 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. C3×#475 | C2 | semidirect |
| 4. #5094 | C2 | semidirect |
| 5. #5021 | C2 | semidirect |
| 7. #4856 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 11. #4797 | C2 | semidirect |
| 53. #475 | D3 | semidirect |
| 246. C3 | #3237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #5578 | 2 |
| C3×#475 | 2 |
| #5094 | 2 |
| #5021 | 2 |
| #4868 | 2 |
| #4856 | 2 |
| #4850 | 2 |
| #4835 | 2 |
| #4814 | 2 |
| #4797 | 2 |
| #3237 | 3 |