Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 171 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. #11721835 | C2 | semidirect |
| 3. #11720577 | C2 | semidirect |
| 9. C22×C3⋊Dic9 | C22 | semidirect |
| 11. #88551 | C22 | semidirect |
| 116. C3×C9 | #458 | semidirect |
| 167. C9 | #5243 | semidirect |
| 192. C3 | #10588923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(5,𝔽2) | 2 |
| #11721835 | 2 |
| #11720577 | 2 |
| #10592942 | 3 |
| #10588923 | 3 |