Finite Group DatabasebetaFinite Group Databasebeta← C2×C9×(C3⋊Dic3)⋊C3 #14517414
Order 1944.
434 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 145 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. C9×(C3⋊Dic3)⋊C3 | C2 | direct (N × H) |
| 3. C2×C9×C3⋊Dic3 | C3 | semidirect |
| 6. C2×(C3⋊Dic3)⋊C9 | C3 | semidirect |
| 7. C2×C9×H(3,𝔽3) | C4 | semidirect |
| 13. C9×C3⋊Dic3 | C2×C3 | semidirect |
| 19. (C3⋊Dic3)⋊C9 | C2×C3 | semidirect |
| 20. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 24. C2×(C3⋊Dic3)⋊C3 | C9 | direct (N × H) |
| 32. C2×C32×C9 | Dic3 | semidirect |
| 33. C2×C32×C9 | C3×C4 | semidirect |
| 40. C2×C32⋊C9 | C3×C4 | semidirect |
| 60. (C3⋊Dic3)⋊C3 | C2×C9 | direct (N × H) |
| 66. C32×C9 | C2×Dic3 | semidirect |
| 67. C32×C9 | C2×C3×C4 | semidirect |
| 70. C32⋊C9 | C2×C3×C4 | semidirect |
| 72. C2×C3⋊Dic3 | C3×C9 | semidirect |
| 86. C2×H(3,𝔽3) | C4×C9 | semidirect |
| 120. C3⋊Dic3 | C2×C3×C9 | semidirect |
| 135. H(3,𝔽3) | C2×C4×C9 | semidirect |
| 166. C2×C32 | C9×Dic3 | semidirect |
| 167. C2×C32 | C3×C4×C9 | semidirect |
| 180. C2×C9 | (C3⋊Dic3)⋊C3 | direct (N × H) |
| 201. C32 | C2×C9×Dic3 | semidirect |
| 202. C32 | C2×C3×C4×C9 | semidirect |
| 208. C9 | C2×(C3⋊Dic3)⋊C3 | direct (N × H) |
| 233. C2 | C9×(C3⋊Dic3)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×H(3,𝔽3) | 2 |
| C9×(C3⋊Dic3)⋊C3 | 2 |
| C2×C9×C3⋊Dic3 | 3 |
| C2×C3×(C3⋊Dic3)⋊C3 | 3 |
| C2×C3×C9×Dic3 | 3 |
| C2×(C3⋊Dic3)⋊C9 | 3 |