Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
350 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×C9×3−1+2 | C2 | semidirect |
| 2. C2×C9×AGL(1,ℤ/9) | C2 | semidirect |
| 3. C9×3−1+2⋊C4 | C2 | semidirect |
| 6. #611⋊C9 | C3 | semidirect |
| 7. C9×#611 | C3 | semidirect |
| 18. C22×C9⋊C9 | C2×C3 | semidirect |
| 21. C22×C92 | C2×C3 | semidirect |
| 22. C2×D9⋊C9 | C2×C3 | semidirect |
| 23. C2×C9×D9 | C2×C3 | semidirect |
| 24. Dic9⋊C9 | C2×C3 | semidirect |
| 25. C9×Dic9 | C2×C3 | semidirect |
| 26. C9×3−1+2 | D4 | semidirect |
| 29. #611⋊C3 | C9 | direct (N × H) |
| 55. C22×3−1+2 | C2×C9 | semidirect |
| 65. C2×AGL(1,ℤ/9) | C2×C9 | semidirect |
| 70. 3−1+2⋊C4 | C2×C9 | semidirect |
| 77. C9⋊C9 | C3×D4 | semidirect |
| 80. C92 | C3×D4 | semidirect |
| 86. #611 | C3×C9 | semidirect |
| 133. C22×C9 | AGL(1,ℤ/9) | semidirect |
| 134. C22×C9 | C2×C3×C9 | semidirect |
| 135. C2×D9 | C2×C3×C9 | semidirect |
| 138. Dic9 | C2×C3×C9 | semidirect |
| 141. 3−1+2 | D4×C9 | semidirect |
| 203. C9 | #611⋊C3 | direct (N × H) |
| 204. C9 | C3×D4×C9 | semidirect |
| 218. 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 |
|---|---|
| C22×C9×3−1+2 | 2 |
| C2×C9×AGL(1,ℤ/9) | 2 |
| C9×3−1+2⋊C4 | 2 |
| C3×#611⋊C3 | 3 |
| C3×C9×#67 | 3 |
| #611⋊C9 | 3 |
| C9×#611 | 3 |