Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1376 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1376 conjugacy classes of subgroups — too many to draw. Only its 292 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. C3×H(3,𝔽3)×C43⋊C3 | C3 | semidirect |
| 2. C32×C9×C43⋊C3 | C3 | semidirect |
| 3. C3×#16812513 | C3 | semidirect |
| 4. C3×#16812512 | C3 | semidirect |
| 5. #732×C43⋊C3 | C3 | direct (N × H) |
| 6. C3×C43×#732 | C3 | semidirect |
| 10. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 12. H(3,𝔽3)×C43⋊C3 | C32 | semidirect |
| 13. C32×C43⋊C9 | C32 | semidirect |
| 17. C3×C9×C43⋊C3 | C32 | semidirect |
| 18. #16812513 | C32 | semidirect |
| 19. #16812512 | C32 | semidirect |
| 20. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 21. C32×C9×C43 | C32 | semidirect |
| 22. C43×#732 | C32 | semidirect |
| 33. C32⋊(C43⋊C3) | C33 | semidirect |
| 36. C3×C43⋊C9 | C33 | semidirect |
| 42. H(3,𝔽3)×C43 | C33 | semidirect |
| 45. C3×C9×C43 | C33 | semidirect |
| 59. C3×C43⋊C3 | #732 | direct (N × H) |
| 69. C3×#732 | C43⋊C3 | direct (N × H) |
| 73. C3×C43 | C3×#732 | semidirect |
| 77. C43⋊C3 | C3×#732 | direct (N × H) |
| 84. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 90. C32×C9 | C3×C43⋊C3 | semidirect |
| 93. #732 | C3×C43⋊C3 | direct (N × H) |
| 94. C43 | C32×#732 | semidirect |
| 109. H(3,𝔽3) | C32×C43⋊C3 | semidirect |
| 117. C3×C9 | C32×C43⋊C3 | semidirect |
| 141. C3 | #732×C43⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32×C9×C43⋊C3 | 3 |
| C3×#16812513 | 3 |
| C3×#16812512 | 3 |
| #732×C43⋊C3 | 3 |
| C3×C43×#732 | 3 |
| C32×#732 | 43 |