Finite Group DatabasebetaFinite Group Databasebeta← C4⋊((C3⋊D3)⋊H(3,𝔽3)) #14517310
Order 1944.
537 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 72 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. C4×C32⋊H(3,𝔽3) | C2 | semidirect |
| 3. C32×C4⋊(C3⋊D3) | C3 | semidirect |
| 5. C3×C4⋊((C3⋊D3)⋊C3) | C3 | semidirect |
| 8. C2×C32×C3⋊D3 | C2×C3 | semidirect |
| 9. C34×C4 | C2×C3 | semidirect |
| 11. C2×C3×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 14. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 15. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 16. C32⋊H(3,𝔽3) | D4 | semidirect |
| 45. C33×C4 | C3×D3 | semidirect |
| 56. C34 | C3×D4 | semidirect |
| 59. C3×H(3,𝔽3) | D12 | semidirect |
| 60. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 63. C4⋊(C3⋊D3) | H(3,𝔽3) | semidirect |
| 95. C2×C3⋊D3 | C2×H(3,𝔽3) | semidirect |
| 122. C32×C4 | (C3⋊D3)⋊C3 | semidirect |
| 123. C32×C4 | C2×H(3,𝔽3) | semidirect |
| 133. C33 | C3×D12 | semidirect |
| 215. C32 | C4⋊((C3⋊D3)⋊C3) | semidirect |
| 216. C32 | D4×H(3,𝔽3) | semidirect |
| 235. C4 | (C3⋊D3)⋊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 |
| C4×C32⋊H(3,𝔽3) | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| D12×H(3,𝔽3) | 3 |
| C3×C4⋊((C3⋊D3)⋊C3) | 3 |