Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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. #5732 | C2 | semidirect |
| 3. C3×#498 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5087 | C2 | semidirect |
| 6. #4868 | C2 | semidirect |
| 7. #4866 | C2 | semidirect |
| 8. #4864 | C2 | semidirect |
| 9. #4860 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. C8×D12 | C2 | semidirect |
| 44. #498 | D3 | semidirect |
| 235. C3 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5734 | 2 |
| #5732 | 2 |
| C3×#498 | 2 |
| #5091 | 2 |
| #5087 | 2 |
| #4868 | 2 |
| #4866 | 2 |
| #4864 | 2 |
| #4860 | 2 |
| C4×#204 | 2 |
| C8×D12 | 2 |
| #3340 | 3 |