Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
356 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 2. C3×#66323 | C2 | direct (N × H) |
| 5. C2×#66323 | C3 | direct (N × H) |
| 6. C2×C3×#731 | C4 | semidirect |
| 15. #66323 | C2×C3 | direct (N × H) |
| 16. C3×#731 | C2×C4 | semidirect |
| 26. C2×C32×C9 | Dic3 | semidirect |
| 30. C2×#731 | C3×C4 | semidirect |
| 50. C32×C9 | C2×Dic3 | semidirect |
| 52. #731 | C2×C3×C4 | semidirect |
| 79. C2×C3×C9 | C3×Dic3 | semidirect |
| 106. C3×C9 | C2×C3×Dic3 | semidirect |
| 157. C2×C3 | #66323 | direct (N × H) |
| 167. C3 | C2×#66323 | direct (N × H) |
| 169. C2 | C3×#66323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#731 | 2 |
| C3×#66323 | 2 |
| C2×C3×#1084 | 3 |
| C2×C3×C9×Dic3 | 3 |
| C2×#66323 | 3 |