Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
781 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 781 conjugacy classes of subgroups — too many to draw. Only its 126 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. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 3. C3×Dic3×H(3,𝔽3) | C2 | semidirect |
| 4. C32×D3×Dic3 | C3 | semidirect |
| 8. C3×D3×H(3,𝔽3) | C4 | semidirect |
| 10. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 11. C33×Dic3 | C2×C3 | semidirect |
| 20. Dic3×H(3,𝔽3) | D3 | direct (N × H) |
| 21. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 28. C33×D3 | C3×C4 | semidirect |
| 37. D3×H(3,𝔽3) | Dic3 | direct (N × H) |
| 53. C32×Dic3 | C3×D3 | semidirect |
| 60. C34 | C2×C3×C4 | semidirect |
| 65. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 66. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 72. D3×Dic3 | H(3,𝔽3) | direct (N × H) |
| 88. C32×D3 | C3×Dic3 | semidirect |
| 113. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 123. C3×Dic3 | C2×H(3,𝔽3) | semidirect |
| 133. C33 | C3×C4×D3 | semidirect |
| 134. C33 | C2×C3×Dic3 | semidirect |
| 140. H(3,𝔽3) | D3×Dic3 | direct (N × H) |
| 176. C3×D3 | C4×H(3,𝔽3) | semidirect |
| 194. Dic3 | D3×H(3,𝔽3) | direct (N × H) |
| 214. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 215. C32 | C3×D3×Dic3 | semidirect |
| 235. D3 | Dic3×H(3,𝔽3) | direct (N × H) |
| 247. C3 | C4×D3×H(3,𝔽3) | semidirect |
| 248. C3 | C2×Dic3×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×H(3,𝔽3) | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C32×D3×Dic3 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |
| C4×D3×H(3,𝔽3) | 3 |