Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
274 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 27 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. H(3,𝔽3)⋊(C22⋊C9) | C2 | semidirect |
| 8. C32×C22⋊C9 | D3 | semidirect |
| 13. C22×#272 | C9 | semidirect |
| 28. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 58. #272 | C22⋊C9 | semidirect |
| 95. H(3,𝔽3) | C2×C22⋊C9 | semidirect |
| 191. C22 | #272⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)⋊(C22⋊C9) | 2 |
| C22×C3×#272 | 3 |
| C3×D3×C22⋊C9 | 3 |
| #272⋊C9 | 4 |