Finite Group DatabasebetaFinite Group Databasebeta← C3×((C22⋊C9)⋊C2)⋊C9 #14517965
Order 1944.
255 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 52 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. C3×(C22⋊C9)⋊C9 | C2 | semidirect |
| 4. ((C22⋊C9)⋊C2)⋊C9 | C3 | direct (N × H) |
| 12. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 15. C3×(C22⋊C9)⋊C2 | C9 | semidirect |
| 35. C3×C22⋊C9 | C2×C9 | semidirect |
| 47. (C22⋊C9)⋊C2 | C3×C9 | semidirect |
| 75. C22⋊C9 | C2×C3×C9 | semidirect |
| 106. C22×C3 | D9⋊C9 | semidirect |
| 133. C22 | C3×D9⋊C9 | semidirect |
| 137. C3 | ((C22⋊C9)⋊C2)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×(C22⋊C9)⋊C9 | 2 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C3×C9×#67 | 3 |
| ((C22⋊C9)⋊C2)⋊C9 | 3 |
| C3×D9⋊C9 | 4 |