Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
594 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 105 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⋊#4185 | C2 | semidirect |
| 2. C3×C4×#732 | C2 | semidirect |
| 10. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 11. C32×C4×C9 | D3 | semidirect |
| 13. C4×#732 | D3 | semidirect |
| 14. C3×#732 | D4 | semidirect |
| 34. C4×H(3,𝔽3) | C3⋊D3 | semidirect |
| 37. C3×C4×C9 | C3⋊D3 | semidirect |
| 38. C3×H(3,𝔽3) | D12 | semidirect |
| 39. C32×C9 | D12 | semidirect |
| 40. #732 | D12 | semidirect |
| 75. H(3,𝔽3) | C4⋊(C3⋊D3) | semidirect |
| 78. C3×C9 | C4⋊(C3⋊D3) | semidirect |
| 103. C3×C4 | #4185 | semidirect |
| 123. C4 | C3⋊#4185 | semidirect |
| 127. C3 | C4⋊#4185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#4185 | 2 |
| C3×C4×#732 | 2 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 3 |
| C3×C4⋊(C3⋊D9) | 3 |
| C4⋊#4185 | 3 |