Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
400 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 106 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⋊#66324 | C2 | direct (N × H) |
| 3. C2×C3⋊(C3⋊Dic9) | C3 | semidirect |
| 6. C2×C3×#731 | C4 | semidirect |
| 11. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 16. C3×#731 | C2×C4 | semidirect |
| 28. C2×C32×C9 | C3×C4 | semidirect |
| 32. C2×#731 | Dic3 | semidirect |
| 54. C32×C9 | C2×C3×C4 | semidirect |
| 56. #731 | C2×Dic3 | semidirect |
| 84. C2×C3×C9 | C3×Dic3 | semidirect |
| 112. C3×C9 | C2×C3×Dic3 | semidirect |
| 165. C2×C3 | #66324 | semidirect |
| 175. C3 | C2×#66324 | semidirect |
| 177. C2 | C3⋊#66324 | 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⋊#66324 | 2 |
| C2×C3⋊(C3⋊Dic9) | 3 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 3 |
| C2×#66324 | 3 |