Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
300 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 49 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. C3×2−1+4⋊C9 | C2 | semidirect |
| 2. #1010⋊C9 | C2 | semidirect |
| 3. C3⋊(#131⋊C9) | C2 | semidirect |
| 19. 2−1+4⋊C9 | D3 | semidirect |
| 26. #5838 | C9 | semidirect |
| 54. C3×2−1+4 | C2×C9 | semidirect |
| 56. #1010 | C2×C9 | semidirect |
| 64. #948 | C2×C9 | semidirect |
| 144. 2−1+4 | D3×C9 | semidirect |
| 277. C3 | #578⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×2−1+4⋊C9 | 2 |
| #1010⋊C9 | 2 |
| C3⋊(#131⋊C9) | 2 |
| C3×#5838 | 3 |
| #578⋊C9 | 3 |
| C9×#213 | 4 |