Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #5733 | C2 | semidirect |
| 2. C3×#498 | C2 | semidirect |
| 3. #5089 | C2 | semidirect |
| 4. #4869 | C2 | semidirect |
| 5. #4867 | C2 | semidirect |
| 7. #4864 | C2 | semidirect |
| 8. #4853 | C2 | semidirect |
| 9. #4852 | C2 | semidirect |
| 10. #4696 | C2 | semidirect |
| 11. #4689 | C2 | semidirect |
| 41. #498 | D3 | semidirect |
| 214. C3 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5733 | 2 |
| C3×#498 | 2 |
| #5089 | 2 |
| #4869 | 2 |
| #4867 | 2 |
| #4865 | 2 |
| #4864 | 2 |
| #4853 | 2 |
| #4852 | 2 |
| #4696 | 2 |
| #4689 | 2 |
| #3173 | 3 |