Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
211 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4⋊AGL(1,ℤ/9) |
| commutator, hypocenter | C9×A4 | C2×C9 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C9⋊C9 | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C3×C9⋊S4 | C3 |
| cosocle | C3×C9×A4 | C2×C3 |
| LCS | G ▷ C9×A4 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×C9⋊C9 | C2 | semidirect |
| 10. C22×C9⋊C9 | D3 | semidirect |
| 14. (C22⋊C9)⋊C9 | D3 | semidirect |
| 18. C9⋊S4 | C9 | semidirect |
| 42. C9×A4 | C2×C9 | semidirect |
| 51. C9⋊C9 | S4 | semidirect |
| 78. C22×C9 | D3×C9 | semidirect |
| 83. C22⋊C9 | D3×C9 | semidirect |
| 119. A4 | D9⋊C9 | semidirect |
| 134. C9 | C9×S4 | semidirect |
| 143. C22 | C3⋊(D9⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C9⋊C9 | 2 |
| C3×C9⋊S4 | 3 |
| C9×C3⋊S4 | 3 |
| ((C22⋊C9)⋊C2)⋊C9 | 3 |
| #611⋊C9 | 3 |
| C3⋊(D9⋊C9) | 4 |