Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 29. #4703 | C9 | direct (N × H) |
| 107. C3×C9 | #491 | semidirect |
| 150. C9 | #4703 | direct (N × H) |
| 169. C3 | C9×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#870 | 2 |
| C9×#869 | 2 |
| C3×C9×#97 | 2 |
| C9×#816 | 2 |
| C3×#4703 | 3 |
| C9×#491 | 3 |