Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5721 | C2 | semidirect |
| 3. C3×#487 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 7. #4799 | C2 | semidirect |
| 9. #4790 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 45. #487 | D3 | semidirect |
| 226. C3 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5732 | 2 |
| #5721 | 2 |
| C3×#487 | 2 |
| #5090 | 2 |
| #5087 | 2 |
| #4800 | 2 |
| #4799 | 2 |
| #4798 | 2 |
| #4790 | 2 |
| C4×#204 | 2 |
| C8×Dic6 | 2 |
| #3364 | 3 |