Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×Dic6 | C2 | semidirect |
| 3. C22×C3×M16 | C2 | semidirect |
| 4. C2×#909 | C2 | direct (N × H) |
| 5. C22×Dic12 | C2 | semidirect |
| 6. C22×#204 | C2 | semidirect |
| 19. C22×Dic6 | C22 | semidirect |
| 20. C2×C3×M16 | C22 | semidirect |
| 22. #909 | C22 | direct (N × H) |
| 23. C2×Dic12 | C22 | semidirect |
| 24. C2×#204 | C22 | semidirect |
| 30. C22×M16 | D3 | semidirect |
| 52. C2×Dic6 | C23 | semidirect |
| 53. C3×M16 | C23 | semidirect |
| 55. Dic12 | C23 | semidirect |
| 56. #204 | C23 | semidirect |
| 72. C2×M16 | C2×D3 | semidirect |
| 121. M16 | C22×D3 | semidirect |
| 124. C22×C3 | #137 | semidirect |
| 158. C2×C3 | C2×#137 | semidirect |
| 164. C22 | #909 | direct (N × H) |
| 172. C3 | C22×#137 | semidirect |
| 175. C2 | C2×#909 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C23×Dic6 | 2 |
| C22×C3×M16 | 2 |
| C2×#909 | 2 |
| C22×Dic12 | 2 |
| C22×#204 | 2 |
| C22×#137 | 3 |