Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
2637 conjugacy classes of subgroups; only the 672 normal subgroups are shown.
This group has 2637 conjugacy classes of subgroups — too many to draw. Only its 672 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. C22×C32×H(3,𝔽3) | C2 | semidirect |
| 2. C2×C3×D3×H(3,𝔽3) | C2 | direct (N × H) |
| 3. C22×C33×D3 | C3 | semidirect |
| 5. C22×D3×H(3,𝔽3) | C3 | direct (N × H) |
| 6. C2×C32×H(3,𝔽3) | C22 | semidirect |
| 7. C3×D3×H(3,𝔽3) | C22 | direct (N × H) |
| 8. C22×C34 | C2×C3 | semidirect |
| 9. C2×C33×D3 | C2×C3 | semidirect |
| 13. C22×C3×H(3,𝔽3) | D3 | direct (N × H) |
| 14. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 15. C2×D3×H(3,𝔽3) | C2×C3 | direct (N × H) |
| 16. C32×H(3,𝔽3) | C23 | semidirect |
| 20. C22×C32×D3 | C32 | semidirect |
| 22. C2×C34 | C22×C3 | semidirect |
| 23. C33×D3 | C22×C3 | semidirect |
| 27. C2×C3×H(3,𝔽3) | C2×D3 | direct (N × H) |
| 28. C2×C3×H(3,𝔽3) | C22×C3 | semidirect |
| 29. D3×H(3,𝔽3) | C22×C3 | direct (N × H) |
| 35. C22×C33 | C3×D3 | semidirect |
| 37. C22×C33 | C2×C32 | semidirect |
| 40. C2×C32×D3 | C2×C32 | semidirect |
| 43. C22×H(3,𝔽3) | C3×D3 | direct (N × H) |
| 44. C34 | C23×C3 | semidirect |
| 47. C3×H(3,𝔽3) | C22×D3 | direct (N × H) |
| 48. C3×H(3,𝔽3) | C23×C3 | semidirect |
| 53. C22×C3×D3 | H(3,𝔽3) | direct (N × H) |
| 60. C2×C33 | C2×C3×D3 | semidirect |
| 62. C2×C33 | C22×C32 | semidirect |
| 65. C32×D3 | C22×C32 | semidirect |
| 68. C2×H(3,𝔽3) | C2×C3×D3 | direct (N × H) |
| 80. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 82. C22×C32 | C32×D3 | semidirect |
| 85. C2×C3×D3 | C2×H(3,𝔽3) | direct (N × H) |
| 91. C33 | C22×C3×D3 | semidirect |
| 93. C33 | C23×C32 | semidirect |
| 95. H(3,𝔽3) | C22×C3×D3 | direct (N × H) |
| 99. C22×D3 | C3×H(3,𝔽3) | direct (N × H) |
| 111. C2×C32 | C22×H(3,𝔽3) | semidirect |
| 113. C2×C32 | C2×C32×D3 | semidirect |
| 116. C3×D3 | C22×H(3,𝔽3) | direct (N × H) |
| 125. C22×C3 | D3×H(3,𝔽3) | direct (N × H) |
| 126. C22×C3 | C2×C3×H(3,𝔽3) | semidirect |
| 128. C2×D3 | C2×C3×H(3,𝔽3) | direct (N × H) |
| 137. C32 | C23×H(3,𝔽3) | semidirect |
| 139. C32 | C22×C32×D3 | semidirect |
| 149. C2×C3 | C2×D3×H(3,𝔽3) | direct (N × H) |
| 150. C2×C3 | C22×C3×H(3,𝔽3) | semidirect |
| 152. D3 | C22×C3×H(3,𝔽3) | direct (N × H) |
| 154. C22 | C3×D3×H(3,𝔽3) | direct (N × H) |
| 159. C3 | C22×D3×H(3,𝔽3) | direct (N × H) |
| 160. C3 | C23×C3×H(3,𝔽3) | semidirect |
| 163. C2 | C2×C3×D3×H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×H(3,𝔽3) | 2 |
| C2×C3×D3×H(3,𝔽3) | 2 |
| C22×C33×D3 | 3 |
| C23×C3×H(3,𝔽3) | 3 |
| C22×D3×H(3,𝔽3) | 3 |