Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 3. #4873 | C2 | semidirect |
| 5. #4503 | C2 | semidirect |
| 6. Dic3×C16 | C2 | semidirect |
| 7. #4490 | C2 | semidirect |
| 16. #827 | C4 | semidirect |
| 42. Dic12 | C2×C4 | semidirect |
| 44. C3⋊C16 | C2×C4 | semidirect |
| 99. Dic3 | SD32 | semidirect |
| 130. C3 | C4×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×D8 | 2 |
| C2×#827 | 2 |
| #4873 | 2 |
| C3×#357 | 2 |
| #4503 | 2 |
| Dic3×C16 | 2 |
| #4490 | 2 |
| C4×SD32 | 3 |