Finite Group DatabasebetaFinite Group Databasebeta← H(3,𝔽3)×C4⋊(C3⋊D3) #14518921
Order 1944.
1104 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 147 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×C3⋊D3×H(3,𝔽3) | C2 | semidirect |
| 2. C32×C4×H(3,𝔽3) | C2 | semidirect |
| 3. C32×C4⋊(C3⋊D3) | C3 | semidirect |
| 7. C2×C32×C3⋊D3 | C2×C3 | semidirect |
| 8. C34×C4 | C2×C3 | semidirect |
| 11. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 12. C32×H(3,𝔽3) | D4 | semidirect |
| 28. C33×C4 | C3×D3 | semidirect |
| 33. C4×H(3,𝔽3) | C3⋊D3 | semidirect |
| 34. C34 | C3×D4 | semidirect |
| 36. C3×H(3,𝔽3) | D12 | semidirect |
| 38. C4⋊(C3⋊D3) | H(3,𝔽3) | direct (N × H) |
| 54. C2×C3⋊D3 | C2×H(3,𝔽3) | semidirect |
| 63. C32×C4 | C2×H(3,𝔽3) | semidirect |
| 65. C32×C4 | C3×C3⋊D3 | semidirect |
| 69. C33 | C3×D12 | semidirect |
| 73. H(3,𝔽3) | C4⋊(C3⋊D3) | direct (N × H) |
| 96. C3×C4 | D3×H(3,𝔽3) | semidirect |
| 104. C32 | D4×H(3,𝔽3) | semidirect |
| 106. C32 | C3×C4⋊(C3⋊D3) | semidirect |
| 117. C4 | C3⋊D3×H(3,𝔽3) | semidirect |
| 121. C3 | D12×H(3,𝔽3) | 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 |
| C32×C4×H(3,𝔽3) | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| D12×H(3,𝔽3) | 3 |