Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. C3×#500 | C2 | semidirect |
| 3. #5094 | C2 | semidirect |
| 4. #4888 | C2 | semidirect |
| 5. #4887 | C2 | semidirect |
| 6. #4880 | C2 | semidirect |
| 7. C4×Dic12 | C2 | semidirect |
| 30. #500 | D3 | semidirect |
| 160. C3 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5732 | 2 |
| C3×#500 | 2 |
| #5094 | 2 |
| #4888 | 2 |
| #4887 | 2 |
| #4880 | 2 |
| C4×Dic12 | 2 |
| C8×D12 | 2 |
| #3342 | 3 |