Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
335 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 41 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. C9×C22⋊H(3,𝔽3) | C2 | semidirect |
| 6. C22×C32×C9 | D3 | semidirect |
| 9. C3×C9×A4 | D3 | semidirect |
| 16. #6258 | C9 | direct (N × H) |
| 35. C22⋊H(3,𝔽3) | C2×C9 | semidirect |
| 42. C32×C9 | S4 | semidirect |
| 68. C22×C32 | D3×C9 | semidirect |
| 76. C3×A4 | D3×C9 | semidirect |
| 83. C22×C9 | #272 | semidirect |
| 140. C32 | C9×S4 | semidirect |
| 144. C9 | #6258 | direct (N × H) |
| 159. C22 | C9×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊H(3,𝔽3) | 2 |
| C3×#6258 | 3 |
| C3×C9×S4 | 3 |
| C3×C9×#67 | 3 |
| C9×#272 | 4 |