Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 246 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. 3−1+2×C22⋊C9 | C2 | semidirect |
| 4. D9×C22⋊C9 | C3 | semidirect |
| 5. D9⋊(C22⋊C9) | C3 | semidirect |
| 13. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 15. C9×C22⋊C9 | C2×C3 | semidirect |
| 18. C22×AGL(1,ℤ/9) | C9 | semidirect |
| 33. C22×3−1+2 | C2×C9 | semidirect |
| 56. C22×D9 | C3×C9 | semidirect |
| 68. AGL(1,ℤ/9) | C22⋊C9 | direct (N × H) |
| 85. C22×C9 | C2×C3×C9 | semidirect |
| 92. C22⋊C9 | AGL(1,ℤ/9) | direct (N × H) |
| 95. 3−1+2 | C2×C22⋊C9 | semidirect |
| 123. D9 | C3×C22⋊C9 | semidirect |
| 145. C9 | C2×C3×C22⋊C9 | semidirect |
| 159. C22 | C9×AGL(1,ℤ/9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C22⋊C9 | 2 |
| C22×C3×AGL(1,ℤ/9) | 3 |
| C3×D3×C22⋊C9 | 3 |
| D9×C22⋊C9 | 3 |
| D9⋊(C22⋊C9) | 3 |
| C9×AGL(1,ℤ/9) | 4 |