Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
231 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 39 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 | C9×C22⋊C9 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C32⋊C9 | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C9×C22⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757767 | C2 | semidirect |
| 4. C9⋊((C22⋊C9)⋊C2) | C3 | semidirect |
| 17. C9×C22⋊C9 | C2×C3 | semidirect |
| 40. #1094 | D9 | semidirect |
| 100. C22⋊C9 | C3×D9 | semidirect |
| 101. C22⋊C9 | AGL(1,ℤ/9) | semidirect |
| 180. C22 | #92299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757767 | 2 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C3⋊(((C22⋊C9)⋊C2)⋊C3) | 3 |
| C9⋊((C22⋊C9)⋊C2) | 3 |
| #10619746 | 3 |
| #10619630 | 3 |
| #92299 | 4 |