Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
548 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 548 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×#66368 | C2 | semidirect |
| 2. C22×C33×D3 | C3 | semidirect |
| 3. D3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. D3×#1094 | C3 | semidirect |
| 7. C22×C34 | C2×C3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 15. #66368 | D3 | direct (N × H) |
| 27. C33×D3 | A4 | semidirect |
| 38. C22×C33 | C3×D3 | semidirect |
| 49. C22⋊H(3,𝔽3) | C3×D3 | semidirect |
| 52. #1094 | C3×D3 | semidirect |
| 54. C34 | C2×A4 | semidirect |
| 126. C33 | D3×A4 | semidirect |
| 138. C22×D3 | AΣL(1,𝔽27) | semidirect |
| 179. C22×C3 | C2×AΣL(1,𝔽27) | semidirect |
| 220. D3 | #66368 | direct (N × H) |
| 223. C22 | D3×AΣL(1,𝔽27) | semidirect |
| 231. C3 | C2×#66368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66368 | 2 |
| C22×C33×D3 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| D3×#1094 | 3 |
| C2×#66368 | 3 |
| D3×AΣL(1,𝔽27) | 4 |