Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
490 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 115. C3×C9 | #487 | semidirect |
| 159. C9 | #4681 | semidirect |
| 180. C3 | #10588361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C3×C4×C8×C9 | 2 |
| #11720539 | 2 |
| #10592380 | 3 |
| #10588361 | 3 |