Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
903 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 903 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
| 3. C3×C3⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 9. C3×C3⋊#272 | C4 | semidirect |
| 13. C3⋊(C3⋊(C3⋊Dic3)) | D3 | semidirect |
| 15. C3×C3⋊(C3⋊Dic3) | D3 | semidirect |
| 24. C3⋊((C3⋊Dic3)⋊C3) | D3 | semidirect |
| 27. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 50. C3⋊#272 | Dic3 | semidirect |
| 71. C3⋊(C3⋊Dic3) | C3⋊D3 | semidirect |
| 91. C34 | C4×D3 | semidirect |
| 92. C34 | C4×D3 | semidirect |
| 99. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 100. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 211. C33 | D3×Dic3 | semidirect |
| 212. C33 | D3×Dic3 | semidirect |
| 214. C33 | #624 | semidirect |
| 215. C33 | C4×C3⋊D3 | semidirect |
| 223. H(3,𝔽3) | D3×Dic3 | semidirect |
| 325. C32 | #6199 | semidirect |
| 326. C32 | Dic3×C3⋊D3 | semidirect |
| 329. C32 | #6294 | semidirect |
| 364. C3 | #10619885 | semidirect |
| 365. C3 | #10619903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#272 | 2 |
| C3⋊(C3⋊((C3⋊Dic3)⋊C3)) | 2 |
| C3×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| #10620155 | 3 |
| C3⋊D3×C3⋊Dic3 | 3 |
| #10619903 | 3 |
| #10619885 | 3 |