Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
207 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D9⋊A4 |
| commutator, hypocenter | C22×C9 | C2×C3×C9 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×C92 | C2×C3 |
| socle | C22×C32 | C32×D3 |
| prime radical | C3×D9⋊A4 | C3 |
| cosocle | C22×C3×C9 | C2×C32 |
| LCS | G ▷ C22×C9 | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×C9⋊A4 | C2 | semidirect |
| 4. C22×C9×D9 | C3 | semidirect |
| 5. D9⋊(C22⋊C9) | C3 | semidirect |
| 9. C22×C92 | C2×C3 | semidirect |
| 13. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 22. D9⋊A4 | C9 | direct (N × H) |
| 28. C9×D9 | A4 | semidirect |
| 41. C9⋊A4 | C2×C9 | semidirect |
| 50. C92 | C2×A4 | semidirect |
| 55. C22×D9 | C3×C9 | semidirect |
| 79. C22×C9 | AGL(1,ℤ/9) | semidirect |
| 80. C22×C9 | C2×C3×C9 | semidirect |
| 114. D9 | C9×A4 | semidirect |
| 133. C9 | D9⋊A4 | direct (N × H) |
| 134. C9 | C2×C9×A4 | semidirect |
| 146. 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 |
|---|---|
| C9×C9⋊A4 | 2 |
| D3×C9×A4 | 3 |
| C3×D9⋊A4 | 3 |
| C22×C9×D9 | 3 |
| D9⋊(C22⋊C9) | 3 |
| C9×AGL(1,ℤ/9) | 4 |