Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
231 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 231 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. C3×#66365 | C2 | semidirect |
| 2. C22×D3×3−1+2 | C3 | semidirect |
| 4. D3×#1094 | C3 | semidirect |
| 5. C3×D3×C22⋊C9 | C3 | semidirect |
| 8. C22×C3×3−1+2 | C2×C3 | semidirect |
| 12. C3×#1094 | C2×C3 | semidirect |
| 13. C32×C22⋊C9 | C2×C3 | semidirect |
| 18. #66365 | D3 | direct (N × H) |
| 32. D3×3−1+2 | A4 | semidirect |
| 44. C22×3−1+2 | C3×D3 | semidirect |
| 53. #1094 | C3×D3 | semidirect |
| 58. C3×C22⋊C9 | C3×D3 | semidirect |
| 60. C3×3−1+2 | C2×A4 | semidirect |
| 123. 3−1+2 | D3×A4 | semidirect |
| 135. C22×D3 | #731 | semidirect |
| 163. C22×C3 | C2×#731 | semidirect |
| 196. D3 | #66365 | direct (N × H) |
| 199. C22 | D3×#731 | semidirect |
| 205. C3 | C2×#66365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66365 | 2 |
| C22×D3×3−1+2 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| D3×#1094 | 3 |
| C3×D3×C22⋊C9 | 3 |
| C2×#66365 | 3 |
| D3×#731 | 4 |