Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
678 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 162 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. C2×C9⋊#272 | C2 | semidirect |
| 2. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 11. C32×C4×C9 | D3 | semidirect |
| 13. C4×C32⋊C9 | D3 | semidirect |
| 14. C9×H(3,𝔽3) | D4 | semidirect |
| 32. C4×H(3,𝔽3) | D9 | semidirect |
| 38. C32×C9 | D12 | semidirect |
| 39. C32⋊C9 | D12 | semidirect |
| 61. C32×C4 | C3⋊D9 | semidirect |
| 67. C4×C9 | #272 | semidirect |
| 69. H(3,𝔽3) | D36 | semidirect |
| 98. C32 | C4⋊(C3⋊D9) | semidirect |
| 102. C9 | C4⋊#272 | semidirect |
| 112. C4 | C9⋊#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊#272 | 2 |
| C4×C9×H(3,𝔽3) | 2 |
| C4⋊(C3⋊#272) | 3 |
| C3×C4⋊(C3⋊D9) | 3 |
| C4⋊#4181 | 3 |