Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
531 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 531 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. C9⋊#997 | C2 | semidirect |
| 3. C9×#585 | C3 | semidirect |
| 4. #10593125 | C3 | semidirect |
| 24. C9×#41 | A4 | semidirect |
| 33. C22×C4×C9 | A4 | semidirect |
| 62. #585 | 3−1+2 | semidirect |
| 123. #41 | C9⋊A4 | semidirect |
| 132. C22×C4 | C9⋊A4 | semidirect |
| 145. C9 | #5950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊#997 | 2 |
| C3×#5950 | 3 |
| C9×#585 | 3 |
| #10593125 | 3 |
| #88683 | 4 |
| C4×C9⋊A4 | 4 |