Finite Group DatabasebetaFinite Group Databasebeta← C22×C3⋊((C3⋊Dic3)⋊C3) #13048941
Order 1296.
942 conjugacy classes of subgroups; only the 278 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 278 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. C2×C3⋊((C3⋊Dic3)⋊C3) | C2 | direct (N × H) |
| 3. C22×C3⋊(C3⋊Dic3) | C3 | semidirect |
| 6. C22×C3×H(3,𝔽3) | C4 | semidirect |
| 8. C3⋊((C3⋊Dic3)⋊C3) | C22 | direct (N × H) |
| 12. C2×C3⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 17. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 26. C22×C33 | Dic3 | semidirect |
| 27. C22×C33 | C3×C4 | semidirect |
| 30. C3⋊(C3⋊Dic3) | C22×C3 | semidirect |
| 34. C22×H(3,𝔽3) | Dic3 | semidirect |
| 37. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 53. C2×C33 | C2×Dic3 | semidirect |
| 54. C2×C33 | C2×C3×C4 | semidirect |
| 59. C2×H(3,𝔽3) | C2×Dic3 | semidirect |
| 76. C22×C32 | C3×Dic3 | semidirect |
| 77. C22×C32 | C3⋊Dic3 | semidirect |
| 87. C33 | C22×Dic3 | semidirect |
| 88. C33 | C22×C3×C4 | semidirect |
| 90. H(3,𝔽3) | C22×Dic3 | semidirect |
| 112. C2×C32 | C2×C3×Dic3 | semidirect |
| 113. C2×C32 | C2×C3⋊Dic3 | semidirect |
| 126. C22×C3 | (C3⋊Dic3)⋊C3 | semidirect |
| 140. C32 | C22×C3×Dic3 | semidirect |
| 141. C32 | C22×C3⋊Dic3 | semidirect |
| 152. C2×C3 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 156. C22 | C3⋊((C3⋊Dic3)⋊C3) | direct (N × H) |
| 163. C3 | C22×(C3⋊Dic3)⋊C3 | semidirect |
| 165. C2 | C2×C3⋊((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 |
|---|---|
| C23×C3×H(3,𝔽3) | 2 |
| C2×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| C22×C3⋊(C3⋊Dic3) | 3 |
| C22×C3×C3⋊Dic3 | 3 |
| C22×(C3⋊Dic3)⋊C3 | 3 |