Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
509 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 509 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×H(3,𝔽3)⋊C9 | C2 | semidirect |
| 2. C2×#272⋊C9 | C2 | direct (N × H) |
| 5. C2×H(3,𝔽3)⋊C9 | C22 | semidirect |
| 6. #272⋊C9 | C22 | direct (N × H) |
| 8. C22×C32×C9 | D3 | semidirect |
| 12. H(3,𝔽3)⋊C9 | C23 | semidirect |
| 16. C22×#272 | C9 | semidirect |
| 19. C2×C32×C9 | C2×D3 | semidirect |
| 29. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 34. C2×#272 | C2×C9 | semidirect |
| 37. C32×C9 | C22×D3 | semidirect |
| 55. C2×H(3,𝔽3) | C22×C9 | semidirect |
| 60. #272 | C22×C9 | semidirect |
| 89. H(3,𝔽3) | C23×C9 | semidirect |
| 165. C22 | #272⋊C9 | direct (N × H) |
| 175. C2 | C2×#272⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(3,𝔽3)⋊C9 | 2 |
| C2×#272⋊C9 | 2 |
| C22×C3×#272 | 3 |
| C22×C3×D3×C9 | 3 |