Finite Group DatabasebetaFinite Group Databasebeta← C32×C4⋊((C3⋊D3)⋊C3) #14518881
Order 1944.
1260 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 270 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 |
|---|---|---|
| 1. C2×C32×(C3⋊D3)⋊C3 | C2 | semidirect |
| 2. C32×C4×H(3,𝔽3) | C2 | semidirect |
| 3. C32×C4⋊(C3⋊D3) | C3 | semidirect |
| 5. C3×C4⋊((C3⋊D3)⋊C3) | C3 | direct (N × H) |
| 8. C2×C32×C3⋊D3 | C2×C3 | semidirect |
| 11. C34×C4 | D3 | semidirect |
| 12. C34×C4 | C2×C3 | semidirect |
| 13. C2×C3×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 15. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 16. C32×H(3,𝔽3) | D4 | semidirect |
| 18. C3×C4⋊(C3⋊D3) | C32 | semidirect |
| 22. C4⋊((C3⋊D3)⋊C3) | C32 | direct (N × H) |
| 32. C2×C3×C3⋊D3 | C2×C32 | semidirect |
| 45. C33×C4 | C3×D3 | semidirect |
| 46. C33×C4 | C2×C32 | semidirect |
| 47. C2×(C3⋊D3)⋊C3 | C2×C32 | semidirect |
| 49. C4×H(3,𝔽3) | C2×C32 | semidirect |
| 51. C34 | D12 | semidirect |
| 52. C34 | C3×D4 | semidirect |
| 54. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 57. C4⋊(C3⋊D3) | C33 | semidirect |
| 82. C2×C3⋊D3 | C2×C33 | semidirect |
| 97. C32×C4 | (C3⋊D3)⋊C3 | semidirect |
| 99. C32×C4 | C32×D3 | semidirect |
| 100. C32×C4 | C2×C33 | semidirect |
| 110. C33 | C3×D12 | semidirect |
| 111. C33 | C32×D4 | semidirect |
| 113. H(3,𝔽3) | C32×D4 | semidirect |
| 148. C3×C4 | C3×(C3⋊D3)⋊C3 | semidirect |
| 161. C32 | C4⋊((C3⋊D3)⋊C3) | direct (N × H) |
| 163. C32 | C32×D12 | semidirect |
| 164. C32 | C33×D4 | semidirect |
| 178. C4 | C32×(C3⋊D3)⋊C3 | semidirect |
| 184. C3 | C3×C4⋊((C3⋊D3)⋊C3) | 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×C4×H(3,𝔽3) | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| C33×D12 | 3 |
| C3×C4⋊((C3⋊D3)⋊C3) | 3 |