Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1140 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 115 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⋊(C3⋊((C3⋊Dic3)⋊C3)) | C2 | semidirect |
| 6. C32×#272 | C4 | semidirect |
| 9. C3⋊(C3⋊(C3⋊Dic3)) | D3 | semidirect |
| 14. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 26. C3×#272 | Dic3 | semidirect |
| 42. C34 | C4×D3 | semidirect |
| 45. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 66. #272 | C3⋊Dic3 | semidirect |
| 86. C33 | D3×Dic3 | semidirect |
| 91. H(3,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 127. C32 | #6199 | semidirect |
| 128. C32 | D3×C3⋊Dic3 | semidirect |
| 147. C3 | #10619903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#272 | 2 |
| C3⋊(C3⋊((C3⋊Dic3)⋊C3)) | 2 |
| D3×C3⋊(C3⋊Dic3) | 3 |
| #10619903 | 3 |