Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
351 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 351 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×#66363 | C2 | semidirect |
| 2. C32×D3×A4 | C3 | semidirect |
| 3. C22×D3×H(3,𝔽3) | C3 | semidirect |
| 4. D3×#1094 | C3 | semidirect |
| 7. C33×A4 | C2×C3 | semidirect |
| 8. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 15. #66363 | D3 | direct (N × H) |
| 29. D3×H(3,𝔽3) | A4 | semidirect |
| 42. C32×A4 | C3×D3 | semidirect |
| 47. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 50. #1094 | C3×D3 | semidirect |
| 54. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 126. H(3,𝔽3) | D3×A4 | semidirect |
| 131. C22×D3 | AΣL(1,𝔽27) | semidirect |
| 167. C22×C3 | C2×AΣL(1,𝔽27) | semidirect |
| 208. D3 | #66363 | direct (N × H) |
| 211. C22 | D3×AΣL(1,𝔽27) | semidirect |
| 219. C3 | C2×#66363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66363 | 2 |
| C32×D3×A4 | 3 |
| C22×D3×H(3,𝔽3) | 3 |
| D3×#1094 | 3 |
| C2×#66363 | 3 |
| D3×AΣL(1,𝔽27) | 4 |