Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
270 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 36 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. #11757830 | C2 | semidirect |
| 2. C22×C32×D9 | C3 | semidirect |
| 4. C3×D9⋊A4 | C3 | semidirect |
| 6. C22×C32×C9 | C2×C3 | semidirect |
| 10. C3×C9⋊A4 | C2×C3 | semidirect |
| 24. C32×D9 | A4 | semidirect |
| 44. C32×C9 | C2×A4 | semidirect |
| 52. C22×D9 | H(3,𝔽3) | semidirect |
| 72. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 83. C22×C9 | C2×H(3,𝔽3) | semidirect |
| 119. D9 | C22⋊H(3,𝔽3) | semidirect |
| 138. C32 | D9⋊A4 | semidirect |
| 143. C9 | C2×C22⋊H(3,𝔽3) | semidirect |
| 159. C22 | D9⋊H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757830 | 2 |
| C22×C32×D9 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| C3×D9⋊A4 | 3 |
| D9⋊H(3,𝔽3) | 4 |