Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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. C22×#3746 | C3 | semidirect |
| 34. #3746 | A4 | direct (N × H) |
| 36. C32×A4 | Q16 | semidirect |
| 82. C22×C32 | C3×Q16 | semidirect |
| 84. C3×A4 | Dic12 | semidirect |
| 132. C22×C3 | C3×Dic12 | semidirect |
| 134. A4 | #3746 | direct (N × H) |
| 144. C32 | A4×Q16 | semidirect |
| 163. C22 | C3×#3746 | semidirect |
| 170. C3 | A4×Dic12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#634 | 2 |
| C32×C8×A4 | 2 |
| C22×#3746 | 3 |
| A4×Dic12 | 3 |
| C3×#3746 | 4 |