Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
251 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 251 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×#66357 | C2 | semidirect |
| 2. C22×C3×D3×C9 | C3 | semidirect |
| 4. D3×#1094 | C3 | semidirect |
| 7. C22×C32×C9 | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 15. #66357 | D3 | direct (N × H) |
| 28. C3×D3×C9 | A4 | semidirect |
| 39. C22×C3×C9 | C3×D3 | semidirect |
| 47. #1094 | C3×D3 | semidirect |
| 51. C32×C9 | C2×A4 | semidirect |
| 111. C3×C9 | D3×A4 | semidirect |
| 114. C22×D3 | #731 | semidirect |
| 141. C22×C3 | C2×#731 | semidirect |
| 172. D3 | #66357 | direct (N × H) |
| 175. C22 | D3×#731 | semidirect |
| 181. C3 | C2×#66357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66357 | 2 |
| C22×C3×D3×C9 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| D3×#1094 | 3 |
| C2×#66357 | 3 |
| D3×#731 | 4 |