Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
210 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 210 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. #4492 | C9 | direct (N × H) |
| 87. Dic12 | C4×C9 | semidirect |
| 107. C3×C9 | #358 | semidirect |
| 157. C9 | #4492 | direct (N × H) |
| 180. 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 |
| C3×C9×#107 | 2 |
| C2×C9×C3⋊C16 | 2 |
| C3×#4492 | 3 |
| C9×#358 | 3 |