Finite Group DatabasebetaFinite Group Databasebeta← C3×C3⋊(((C22⋊C9)⋊C2)⋊C3) #14519209
Order 1944.
664 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 70 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 | C3⋊(((C22⋊C9)⋊C2)⋊C3) |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#1094 | C2 | semidirect |
| 3. C3×C3⋊((C22⋊C9)⋊C2) | C3 | semidirect |
| 4. C3⋊(((C22⋊C9)⋊C2)⋊C3) | C3 | direct (N × H) |
| 13. C3×#1094 | D3 | semidirect |
| 14. C3×#1094 | C2×C3 | semidirect |
| 16. C32×C22⋊C9 | C2×C3 | semidirect |
| 22. C3⋊((C22⋊C9)⋊C2) | C32 | semidirect |
| 48. #1094 | C3×D3 | semidirect |
| 54. C3×C22⋊C9 | C3×D3 | semidirect |
| 55. C3×C22⋊C9 | C2×C32 | semidirect |
| 96. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 113. C22⋊C9 | C32×D3 | semidirect |
| 165. C22×C3 | C3×AGL(1,ℤ/9) | semidirect |
| 166. C22×C3 | C3⋊AGL(1,ℤ/9) | semidirect |
| 183. C32 | ((C22⋊C9)⋊C2)⋊C3 | semidirect |
| 204. C22 | C3×C3⋊AGL(1,ℤ/9) | semidirect |
| 210. C3 | C3×((C22⋊C9)⋊C2)⋊C3 | semidirect |
| 211. C3 | C3⋊(((C22⋊C9)⋊C2)⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1094 | 2 |
| C32×#638 | 3 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C3⋊(((C22⋊C9)⋊C2)⋊C3) | 3 |
| C3×((C22⋊C9)⋊C2)⋊C3 | 3 |
| C3×C3⋊AGL(1,ℤ/9) | 4 |