Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#88521 | C2 | semidirect |
| 4. C3×C9×#106 | C2 | semidirect |
| 5. #11720527 | C2 | semidirect |
| 25. C9×#106 | D3 | semidirect |
| 72. C3×#106 | D9 | semidirect |
| 139. #106 | C3⋊D9 | semidirect |
| 141. C3×C9 | #470 | semidirect |
| 196. C9 | #4867 | semidirect |
| 222. C3 | #10588547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| C2×#88521 | 2 |
| #11721753 | 2 |
| C3×C9×#106 | 2 |
| #11720527 | 2 |
| #10592566 | 3 |
| #10588547 | 3 |