Finite Group DatabasebetaFinite Group Databasebeta← C3×C3⋊(C3⋊((C22⋊C9)⋊C2)) #14519223
Order 1944.
942 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 158 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⋊(C3⋊((C22⋊C9)⋊C2)) |
| commutator, cosocle, hypocenter | C32×C22⋊C9 | C2×C3 |
| Frattini | C3 | C3×C3⋊(C3⋊S4) |
| Fitting, socle | C22×C34 | D3 |
| LCS | G ▷ C32×C22⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C33×C22⋊C9 | C2 | semidirect |
| 3. C3⋊(C3⋊((C22⋊C9)⋊C2)) | C3 | direct (N × H) |
| 11. C32×C22⋊C9 | D3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 25. C22×C33 | D9 | semidirect |
| 36. C3×C22⋊C9 | C3×D3 | semidirect |
| 37. C3×C22⋊C9 | C3⋊D3 | semidirect |
| 61. C22×C32 | C3×D9 | semidirect |
| 62. C22×C32 | C3⋊D9 | semidirect |
| 74. C22⋊C9 | C3×C3⋊D3 | semidirect |
| 77. C33 | (C22⋊C9)⋊C2 | semidirect |
| 102. C22×C3 | C3×C3⋊D9 | semidirect |
| 103. C22×C3 | C3⋊(C3⋊D9) | semidirect |
| 113. C32 | C3×(C22⋊C9)⋊C2 | semidirect |
| 114. C32 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 129. C22 | C3×C3⋊(C3⋊D9) | semidirect |
| 133. C3 | C3×C3⋊((C22⋊C9)⋊C2) | semidirect |
| 134. C3 | C3⋊(C3⋊((C22⋊C9)⋊C2)) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊C9 | 2 |
| C3×#6312 | 3 |
| C3⋊(C3⋊((C22⋊C9)⋊C2)) | 3 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C3×C3⋊(C3⋊D9) | 4 |