Finite Group DatabasebetaFinite Group Databasebeta← ((C22⋊C9)⋊C2)⋊H(3,𝔽3) #14517973
Order 1944.
265 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757832 | C2 | semidirect |
| 2. C32×(C22⋊C9)⋊C2 | C3 | semidirect |
| 3. C3×((C22⋊C9)⋊C2)⋊C3 | C3 | semidirect |
| 8. C3×#1094 | C2×C3 | semidirect |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 51. (C22⋊C9)⋊C2 | H(3,𝔽3) | semidirect |
| 71. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 84. C22⋊C9 | C2×H(3,𝔽3) | semidirect |
| 135. C32 | ((C22⋊C9)⋊C2)⋊C3 | semidirect |
| 154. C22 | D9⋊H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757832 | 2 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C3×((C22⋊C9)⋊C2)⋊C3 | 3 |
| #67×H(3,𝔽3) | 3 |
| D9⋊H(3,𝔽3) | 4 |