Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
306 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 63 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×#4175⋊C3 | C2 | semidirect |
| 2. C4×#6909 | C2 | semidirect |
| 3. C4⋊(C3⋊((C3⋊D3)⋊C3)) | C3 | semidirect |
| 5. C4⋊#4175 | C3 | semidirect |
| 8. C2×C3⋊((C3⋊D3)⋊C3) | C2×C3 | semidirect |
| 11. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 12. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 13. C2×#4175 | C2×C3 | semidirect |
| 15. C4×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 16. #6909 | D4 | semidirect |
| 17. C4⋊(C3⋊(C3⋊D3)) | C32 | semidirect |
| 30. C2×C3⋊(C3⋊D3) | C2×C32 | semidirect |
| 36. C33×C4 | C2×C32 | semidirect |
| 48. C3×H(3,𝔽3) | D12 | semidirect |
| 49. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 51. AΣL(1,𝔽27) | C3×D4 | semidirect |
| 98. C33 | C32×D4 | semidirect |
| 169. C4 | #4175⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4175⋊C3 | 2 |
| C4×#6909 | 2 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| C3×C4⋊((C3⋊D3)⋊C3) | 3 |
| C4⋊#4175 | 3 |