Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
281 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 281 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 |
|---|---|---|
| 2. A4×Dic18 | C2 | semidirect |
| 3. A4×C9⋊C8 | C2 | semidirect |
| 5. C22×#3672 | C3 | semidirect |
| 14. C22×Dic18 | C2×C3 | semidirect |
| 20. C22×C9⋊C8 | C2×C3 | semidirect |
| 47. #3672 | A4 | direct (N × H) |
| 51. C9×A4 | SD16 | semidirect |
| 89. Dic18 | C2×A4 | semidirect |
| 91. C9⋊C8 | C2×A4 | semidirect |
| 130. C22×C9 | C3×SD16 | semidirect |
| 209. A4 | #3672 | direct (N × H) |
| 219. C9 | A4×SD16 | semidirect |
| 256. C22 | C3×#3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C9×A4 | 2 |
| A4×Dic18 | 2 |
| A4×C9⋊C8 | 2 |
| A4×#214 | 3 |
| C22×#3672 | 3 |
| C3×#3672 | 4 |