Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
378 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 96 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) |
| 6. C2×C3×#731 | C4 | semidirect |
| 16. C3×#731 | C2×C4 | semidirect |
| 28. C2×C32×C9 | Dic3 | semidirect |
| 32. C2×#731 | Dic3 | semidirect |
| 54. C32×C9 | C2×Dic3 | semidirect |
| 56. #731 | C2×Dic3 | semidirect |
| 84. C2×C3×C9 | C3⋊Dic3 | semidirect |
| 114. C3×C9 | C2×C3⋊Dic3 | semidirect |
| 173. C2×C3 | #66323 | semidirect |
| 183. C3 | C2×#66323 | semidirect |
| 185. 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×C9×C3⋊Dic3 | 3 |
| C2×#66323 | 3 |