Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
235 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 4. C22×Dic36 | C3 | semidirect |
| 35. Dic36 | A4 | direct (N × H) |
| 36. C9×A4 | Q16 | semidirect |
| 85. C22×C9 | C3×Q16 | semidirect |
| 134. A4 | Dic36 | direct (N × H) |
| 144. C9 | A4×Q16 | semidirect |
| 163. C22 | C3×Dic36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×Dic18 | 2 |
| C8×C9×A4 | 2 |
| A4×Dic12 | 3 |
| C22×Dic36 | 3 |
| C3×Dic36 | 4 |