Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
359 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 359 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | D3×A4 |
| commutator, hypocenter | C22×C3 | C2×C92 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×C32×C9 | C2×C3 |
| socle, cosocle | C22×C33 | C2×C32 |
| prime radical | C22×C32×D3 | C32 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C3×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9×C22⋊C9 | C2 | semidirect |
| 12. C9×C22⋊C9 | D3 | direct (N × H) |
| 16. C22×D3×C9 | C9 | semidirect |
| 18. D3×C22⋊C9 | C9 | direct (N × H) |
| 31. C22×C3×C9 | C2×C9 | semidirect |
| 37. C3×C22⋊C9 | C2×C9 | semidirect |
| 61. D3×C9 | C22⋊C9 | direct (N × H) |
| 76. C22×C9 | D3×C9 | semidirect |
| 78. C22⋊C9 | D3×C9 | direct (N × H) |
| 86. C3×C9 | C2×C22⋊C9 | semidirect |
| 90. C22×D3 | C92 | semidirect |
| 113. C22×C3 | C2×C92 | semidirect |
| 126. C9 | D3×C22⋊C9 | direct (N × H) |
| 138. D3 | C9×C22⋊C9 | direct (N × H) |
| 141. C22 | D3×C92 | semidirect |
| 144. C3 | C2×C9×C22⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C22⋊C9 | 2 |
| C22×C3×D3×C9 | 3 |
| C3×D3×C22⋊C9 | 3 |
| C2×C9×C22⋊C9 | 3 |
| D3×C92 | 4 |