Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#869 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4842 | C2 | semidirect |
| 5. #4735 | C2 | semidirect |
| 6. #4694 | C2 | semidirect |
| 7. #4680 | C2 | semidirect |
| 36. #431 | D3 | semidirect |
| 193. C3 | #3227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C2×#869 | 2 |
| C3×#431 | 2 |
| #4842 | 2 |
| #4735 | 2 |
| #4694 | 2 |
| #4680 | 2 |
| #3227 | 3 |