Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 10. C9×Dic12 | C4 | semidirect |
| 27. #4503 | C9 | direct (N × H) |
| 85. Dic12 | C4×C9 | semidirect |
| 105. C3×C9 | #358 | semidirect |
| 153. C9 | #4503 | direct (N × H) |
| 176. C3 | C9×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Dic12 | 2 |
| C2×C3×C9×C16 | 2 |
| C9×#818 | 2 |
| C3×#4503 | 3 |
| C9×#358 | 3 |