Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
671 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×C3⋊#4169 | C2 | semidirect |
| 2. C3×C4×C32⋊C9 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊D9)) | C3 | semidirect |
| 10. C2×C3⋊(C3⋊D9) | C2×C3 | semidirect |
| 12. C32×C4×C9 | C2×C3 | semidirect |
| 15. C4×C32⋊C9 | D3 | semidirect |
| 16. C3×C32⋊C9 | D4 | semidirect |
| 41. C33×C4 | D9 | semidirect |
| 49. C3×C4×C9 | C3×D3 | semidirect |
| 52. C32×C9 | C3×D4 | semidirect |
| 54. C32⋊C9 | D12 | semidirect |
| 101. C32×C4 | C3⋊D9 | semidirect |
| 110. C33 | D36 | semidirect |
| 116. C3×C9 | C3×D12 | semidirect |
| 154. C3×C4 | #4169 | semidirect |
| 169. C32 | C4⋊(C3⋊D9) | semidirect |
| 187. C4 | C3⋊#4169 | semidirect |
| 191. C3 | C4⋊#4169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#4169 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C3×C4⋊(C3⋊(C3⋊D3)) | 3 |
| C4⋊(C3⋊(C3⋊D9)) | 3 |
| C4⋊#4169 | 3 |