Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1403 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1403 conjugacy classes of subgroups — too many to draw. Only its 288 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. C33×D12 | C3 | semidirect |
| 5. D12×H(3,𝔽3) | C3 | direct (N × H) |
| 8. C2×C33×D3 | C2×C3 | semidirect |
| 9. C34×C4 | C2×C3 | semidirect |
| 11. C2×D3×H(3,𝔽3) | 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 |
| 20. C32×D12 | C32 | semidirect |
| 33. C2×C32×D3 | C2×C32 | semidirect |
| 38. C33×C4 | C3×D3 | semidirect |
| 40. C33×C4 | C2×C32 | semidirect |
| 43. C4×H(3,𝔽3) | C3×D3 | semidirect |
| 44. C34 | C3×D4 | semidirect |
| 47. C3×H(3,𝔽3) | D12 | direct (N × H) |
| 48. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 53. C3×D12 | H(3,𝔽3) | direct (N × H) |
| 73. C2×C3×D3 | C2×H(3,𝔽3) | semidirect |
| 83. C32×C4 | C2×H(3,𝔽3) | semidirect |
| 85. C32×C4 | C32×D3 | semidirect |
| 91. C33 | C3×D12 | semidirect |
| 93. C33 | C32×D4 | semidirect |
| 95. H(3,𝔽3) | C3×D12 | direct (N × H) |
| 99. D12 | C3×H(3,𝔽3) | direct (N × H) |
| 121. C2×D3 | C2×C3×H(3,𝔽3) | semidirect |
| 126. C3×C4 | D3×H(3,𝔽3) | semidirect |
| 127. C3×C4 | C2×C3×H(3,𝔽3) | semidirect |
| 137. C32 | D4×H(3,𝔽3) | semidirect |
| 139. C32 | C32×D12 | semidirect |
| 154. C4 | C3×D3×H(3,𝔽3) | semidirect |
| 159. C3 | D12×H(3,𝔽3) | direct (N × H) |
| 160. C3 | C3×D4×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 |
| C33×D12 | 3 |
| C3×D4×H(3,𝔽3) | 3 |
| D12×H(3,𝔽3) | 3 |