Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #5116 | C2 | semidirect |
| 3. C2×#800 | C2 | semidirect |
| 4. C3×C22⋊C16 | C2 | semidirect |
| 5. #4509 | C2 | semidirect |
| 10. C2×Dic12 | C22 | semidirect |
| 14. C2×C3×C16 | C22 | semidirect |
| 15. #818 | C22 | semidirect |
| 22. C22⋊C16 | D3 | semidirect |
| 49. C2×C16 | C2×D3 | semidirect |
| 90. C22×C3 | SD32 | semidirect |
| 130. C22 | #800 | semidirect |
| 137. C3 | #2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| #5116 | 2 |
| C2×#800 | 2 |
| C3×C22⋊C16 | 2 |
| #4509 | 2 |
| #2187 | 3 |