Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
259 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 52 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 | A4×D9 |
| 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×A4×D9 | 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. C92×A4 | C2 | semidirect |
| 4. C22×C9×D9 | C3 | semidirect |
| 5. D9×C22⋊C9 | C3 | semidirect |
| 10. C22×C92 | C2×C3 | semidirect |
| 15. C9×C22⋊C9 | C2×C3 | semidirect |
| 22. A4×D9 | C9 | direct (N × H) |
| 28. C9×D9 | A4 | direct (N × H) |
| 45. C9×A4 | D9 | direct (N × H) |
| 46. C9×A4 | C2×C9 | semidirect |
| 53. C92 | C2×A4 | semidirect |
| 58. C22×D9 | C3×C9 | semidirect |
| 83. C22×C9 | C3×D9 | semidirect |
| 84. C22×C9 | C2×C3×C9 | semidirect |
| 90. C22⋊C9 | C3×D9 | semidirect |
| 122. D9 | C9×A4 | direct (N × H) |
| 131. A4 | C9×D9 | direct (N × H) |
| 144. C9 | A4×D9 | direct (N × H) |
| 145. C9 | C2×C9×A4 | semidirect |
| 157. C22 | C3×C9×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C92×A4 | 2 |
| D3×C9×A4 | 3 |
| C3×A4×D9 | 3 |
| C22×C9×D9 | 3 |
| D9×C22⋊C9 | 3 |
| C3×C9×D9 | 4 |