Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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×#124 | C2 | semidirect |
| 2. C2×#3675⋊C3 | C2 | semidirect |
| 3. C2×#3674⋊C3 | C2 | semidirect |
| 5. C2×#3672⋊C3 | C2 | semidirect |
| 6. #63437⋊C3 | C2 | semidirect |
| 7. C4×3−1+2⋊C8 | C2 | semidirect |
| 9. #10588740 | C3 | semidirect |
| 31. C9×#124 | C2×C3 | semidirect |
| 32. C2×#3675 | C2×C3 | semidirect |
| 33. C2×#3674 | C2×C3 | semidirect |
| 35. C2×#3672 | C2×C3 | semidirect |
| 36. #63437 | C2×C3 | semidirect |
| 37. C4×C9⋊C8 | C2×C3 | semidirect |
| 213. #124 | AGL(1,ℤ/9) | semidirect |
| 215. 3−1+2 | #495 | semidirect |
| 294. C9 | C3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#124 | 2 |
| C2×#3675⋊C3 | 2 |
| C2×#3674⋊C3 | 2 |
| C2×#3673⋊C3 | 2 |
| C2×#3672⋊C3 | 2 |
| #63437⋊C3 | 2 |
| C4×3−1+2⋊C8 | 2 |
| C3×#5059 | 3 |
| #10588740 | 3 |