Finite Group DatabasebetaFinite Group Databasebeta← C32×((C22⋊C9)⋊C2)⋊C3 #14519191
Order 1944.
786 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | ((C22⋊C9)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C22⋊C9 | C2×C33 |
| Frattini | C3 | C33×S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#1094 | C2 | semidirect |
| 3. C32×(C22⋊C9)⋊C2 | C3 | semidirect |
| 4. C3×((C22⋊C9)⋊C2)⋊C3 | C3 | direct (N × H) |
| 10. C3×#1094 | C2×C3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 17. C3×(C22⋊C9)⋊C2 | C32 | semidirect |
| 18. ((C22⋊C9)⋊C2)⋊C3 | C32 | direct (N × H) |
| 34. #1094 | C2×C32 | semidirect |
| 37. C3×C22⋊C9 | C2×C32 | semidirect |
| 47. (C22⋊C9)⋊C2 | C33 | semidirect |
| 63. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 74. C22⋊C9 | C2×C33 | semidirect |
| 103. C22×C3 | C3×AGL(1,ℤ/9) | semidirect |
| 112. C32 | ((C22⋊C9)⋊C2)⋊C3 | direct (N × H) |
| 128. C22 | C32×AGL(1,ℤ/9) | semidirect |
| 132. 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 |
| C33×#67 | 3 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C3×((C22⋊C9)⋊C2)⋊C3 | 3 |
| C32×AGL(1,ℤ/9) | 4 |