Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
224 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 35 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. #11757845 | C2 | semidirect |
| 4. D9×C22⋊C9 | C3 | semidirect |
| 5. D9⋊(C22⋊C9) | C3 | semidirect |
| 12. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 15. C9×C22⋊C9 | C2×C3 | semidirect |
| 57. C22×D9 | 3−1+2 | semidirect |
| 86. C22×C9 | C2×3−1+2 | semidirect |
| 93. C22⋊C9 | AGL(1,ℤ/9) | semidirect |
| 125. D9 | #1094 | semidirect |
| 147. C9 | C2×#1094 | semidirect |
| 161. C22 | #92265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757845 | 2 |
| C22×C3×AGL(1,ℤ/9) | 3 |
| D3×#1094 | 3 |
| D9×C22⋊C9 | 3 |
| D9⋊(C22⋊C9) | 3 |
| #92265 | 4 |