Finite Group DatabasebetaFinite Group Databasebeta← C32×((C3⋊D3)⋊C3)⋊C4 #14518619
Order 1944.
788 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 788 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. C32×#1084 | C2 | semidirect |
| 3. C32×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 6. C3×((C3⋊D3)⋊C3)⋊C4 | C3 | direct (N × H) |
| 8. C32×(C3⋊D3)⋊C3 | C4 | semidirect |
| 11. C32×C3⋊Dic3 | D3 | semidirect |
| 18. C3×#1084 | C2×C3 | semidirect |
| 20. C3×(C3⋊Dic3)⋊C3 | C2×C3 | semidirect |
| 21. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 27. ((C3⋊D3)⋊C3)⋊C4 | C32 | direct (N × H) |
| 31. C32×C3⋊D3 | Dic3 | semidirect |
| 38. C3×(C3⋊D3)⋊C3 | C3×C4 | semidirect |
| 47. C3×C3⋊Dic3 | C3×D3 | semidirect |
| 63. #1084 | C2×C32 | semidirect |
| 65. (C3⋊Dic3)⋊C3 | C2×C32 | semidirect |
| 67. C34 | C4×D3 | semidirect |
| 68. C34 | C2×Dic3 | semidirect |
| 72. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 93. C3×C3⋊D3 | C3×Dic3 | semidirect |
| 104. (C3⋊D3)⋊C3 | C32×C4 | semidirect |
| 119. C3⋊Dic3 | C32×D3 | semidirect |
| 144. C33 | C3×C4×D3 | semidirect |
| 145. C33 | C2×C3×Dic3 | semidirect |
| 150. H(3,𝔽3) | C2×C32×C4 | semidirect |
| 179. C3⋊D3 | C32×Dic3 | semidirect |
| 217. C32 | ((C3⋊D3)⋊C3)⋊C4 | direct (N × H) |
| 219. C32 | C32×C4×D3 | semidirect |
| 220. C32 | C2×C32×Dic3 | semidirect |
| 246. C3 | C3×((C3⋊D3)⋊C3)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×(C3⋊D3)⋊C3 | 2 |
| C32×#1084 | 2 |
| C32×(C3⋊Dic3)⋊C3 | 2 |
| C32×#624 | 3 |
| C32×D3×Dic3 | 3 |
| C3×((C3⋊D3)⋊C3)⋊C4 | 3 |