Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic24 | C2 | semidirect |
| 4. C2×#800 | C2 | semidirect |
| 5. C3×C22⋊C16 | C2 | semidirect |
| 6. #4509 | C2 | semidirect |
| 7. #4503 | C2 | semidirect |
| 30. C22⋊C16 | D3 | semidirect |
| 165. C3 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5116 | 2 |
| C2×Dic24 | 2 |
| C2×#800 | 2 |
| C3×C22⋊C16 | 2 |
| #4509 | 2 |
| #4503 | 2 |
| #2189 | 3 |