Finite Group DatabasebetaFinite Group Databasebeta← C3⋊(C9⋊((C22⋊C9)⋊C2)) #14518112
Order 1944.
654 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C9×C22⋊C9 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C3×C9×C22⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9×C22⋊C9 | C2 | semidirect |
| 10. C9×C22⋊C9 | D3 | semidirect |
| 24. C22×C3×C9 | D9 | semidirect |
| 28. C3×C22⋊C9 | D9 | semidirect |
| 57. C22×C9 | C3⋊D9 | semidirect |
| 59. C22⋊C9 | C3⋊D9 | semidirect |
| 64. C3×C9 | (C22⋊C9)⋊C2 | semidirect |
| 78. C22×C3 | C9⋊D9 | semidirect |
| 91. C9 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 100. C22 | C3⋊(C9⋊D9) | semidirect |
| 102. C3 | C9⋊((C22⋊C9)⋊C2) | 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 |
| C3⋊(C3⋊((C22⋊C9)⋊C2)) | 3 |
| #10619992 | 3 |
| C9⋊((C22⋊C9)⋊C2) | 3 |
| C3⋊(C9⋊D9) | 4 |