Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
356 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 92 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. 3−1+2×#117 | C2 | semidirect |
| 3. #63389⋊C3 | C2 | semidirect |
| 4. #63369⋊C3 | C2 | semidirect |
| 5. #63369⋊C3 | C2 | semidirect |
| 6. #63367⋊C3 | C2 | semidirect |
| 7. #63366⋊C3 | C2 | semidirect |
| 9. #10588684 | C3 | semidirect |
| 29. C9×#117 | C2×C3 | semidirect |
| 31. #63389 | C2×C3 | semidirect |
| 32. #63369 | C2×C3 | semidirect |
| 33. #63369 | C2×C3 | semidirect |
| 34. #63367 | C2×C3 | semidirect |
| 35. #63366 | C2×C3 | semidirect |
| 205. #117 | AGL(1,ℤ/9) | semidirect |
| 211. 3−1+2 | #482 | semidirect |
| 293. C9 | C3×#482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#117 | 2 |
| #63492⋊C3 | 2 |
| #63389⋊C3 | 2 |
| #63369⋊C3 | 2 |
| #63367⋊C3 | 2 |
| #63366⋊C3 | 2 |
| C3×#5003 | 3 |
| #10588684 | 3 |