Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
320 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C3×C9×#101 | C2 | semidirect |
| 3. #11720581 | C2 | semidirect |
| 17. C9×#101 | D3 | semidirect |
| 53. C3×#101 | D9 | semidirect |
| 109. #101 | C3⋊D9 | semidirect |
| 110. C3×C9 | #355 | semidirect |
| 157. C9 | #4477 | semidirect |
| 180. C3 | #10588155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721857 | 2 |
| C3×C9×#101 | 2 |
| #11720581 | 2 |
| #10589343 | 3 |
| #10588155 | 3 |