Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
591 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 87 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. C22×C3×C32⋊C9 | C2 | semidirect |
| 2. C2×C3⋊((C3⋊D3)⋊C9) | C2 | semidirect |
| 3. C3⋊((C3⋊Dic3)⋊C9) | C2 | semidirect |
| 14. C22×C32×C9 | D3 | semidirect |
| 18. C22×C32⋊C9 | D3 | semidirect |
| 21. C3×C32⋊C9 | D4 | semidirect |
| 22. #6312 | C9 | semidirect |
| 45. C22×C33 | C2×C9 | semidirect |
| 48. C2×C3⋊(C3⋊D3) | C2×C9 | semidirect |
| 52. C3⋊(C3⋊Dic3) | C2×C9 | semidirect |
| 60. C22×C3×C9 | C3⋊D3 | semidirect |
| 67. C32×C9 | #67 | semidirect |
| 69. C32⋊C9 | #67 | semidirect |
| 116. C22×C32 | D3×C9 | semidirect |
| 140. C33 | D4×C9 | semidirect |
| 147. C3×C9 | #638 | semidirect |
| 194. C22×C3 | (C3⋊D3)⋊C9 | semidirect |
| 213. C32 | C9×#67 | semidirect |
| 239. C22 | C3⋊((C3⋊D3)⋊C9) | semidirect |
| 245. C3 | #638⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C32⋊C9 | 2 |
| C2×C3⋊((C3⋊D3)⋊C9) | 2 |
| C3⋊((C3⋊Dic3)⋊C9) | 2 |
| C3×#6312 | 3 |
| C9×#638 | 3 |
| #638⋊C9 | 3 |