Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
270 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 89. C3×C9 | #362 | semidirect |
| 123. C9 | #4517 | semidirect |
| 139. C3 | #10588195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C3×C9×M32 | 2 |
| #11720535 | 2 |
| #10589383 | 3 |
| #10588195 | 3 |