Finite Group DatabasebetaFinite Group Databasebeta← C3×C9⋊((C22⋊C9)⋊C2) #14518044
Order 1944.
339 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C9×C22⋊C9 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C9×C22⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9×C22⋊C9 | C2 | semidirect |
| 4. C9⋊((C22⋊C9)⋊C2) | C3 | direct (N × H) |
| 12. C9×C22⋊C9 | C2×C3 | semidirect |
| 28. C22×C3×C9 | D9 | semidirect |
| 34. C3×C22⋊C9 | D9 | semidirect |
| 70. C22×C9 | C3×D9 | semidirect |
| 73. C22⋊C9 | C3×D9 | semidirect |
| 82. C3×C9 | (C22⋊C9)⋊C2 | semidirect |
| 102. C22×C3 | C9⋊D9 | semidirect |
| 118. C9 | C3×(C22⋊C9)⋊C2 | semidirect |
| 129. C22 | C3×C9⋊D9 | semidirect |
| 133. C3 | C9⋊((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 |
|---|---|
| C3×C9×C22⋊C9 | 2 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C3×#6233 | 3 |
| C9⋊((C22⋊C9)⋊C2) | 3 |
| C3×C9⋊D9 | 4 |