Finite Group DatabasebetaFinite Group Databasebeta← D3×C3⋊((C3⋊Dic3)⋊C3) #14518677
Order 1944.
857 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 857 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
| 4. D3×C3⋊(C3⋊Dic3) | C3 | semidirect |
| 9. C3×D3×H(3,𝔽3) | C4 | semidirect |
| 13. C3⋊(C3⋊(C3⋊Dic3)) | C2×C3 | semidirect |
| 15. C3×C3⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 25. C3⋊((C3⋊Dic3)⋊C3) | D3 | direct (N × H) |
| 27. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 40. C33×D3 | Dic3 | semidirect |
| 41. C33×D3 | C3×C4 | semidirect |
| 52. D3×H(3,𝔽3) | Dic3 | semidirect |
| 71. C3⋊(C3⋊Dic3) | C3×D3 | semidirect |
| 91. C34 | C2×Dic3 | semidirect |
| 92. C34 | C2×C3×C4 | semidirect |
| 99. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 100. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 140. C32×D3 | C3×Dic3 | semidirect |
| 141. C32×D3 | C3⋊Dic3 | semidirect |
| 210. C33 | D3×Dic3 | semidirect |
| 211. C33 | C3×C4×D3 | semidirect |
| 213. C33 | C2×C3×Dic3 | semidirect |
| 214. C33 | C2×C3⋊Dic3 | semidirect |
| 222. H(3,𝔽3) | D3×Dic3 | semidirect |
| 271. C3×D3 | (C3⋊Dic3)⋊C3 | semidirect |
| 320. C32 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 322. C32 | C3×D3×Dic3 | semidirect |
| 323. C32 | D3×C3⋊Dic3 | semidirect |
| 345. D3 | C3⋊((C3⋊Dic3)⋊C3) | direct (N × H) |
| 359. C3 | D3×(C3⋊Dic3)⋊C3 | semidirect |
| 360. C3 | C2×C3⋊((C3⋊Dic3)⋊C3) | 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 |
| C3⋊(C3⋊((C3⋊Dic3)⋊C3)) | 2 |
| C3×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| D3×C3⋊(C3⋊Dic3) | 3 |
| C3×D3×C3⋊Dic3 | 3 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 3 |
| D3×(C3⋊Dic3)⋊C3 | 3 |