Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1160 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1160 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. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 3. C32×C9×C43⋊C3 | C3 | semidirect |
| 4. C3×#16812511 | C3 | semidirect |
| 5. C3×#16812510 | C3 | semidirect |
| 6. C3×#16812509 | C3 | semidirect |
| 7. #731×C43⋊C3 | C3 | direct (N × H) |
| 8. C3×C43×#731 | C3 | semidirect |
| 11. C3×#11923958 | C32 | semidirect |
| 15. 3−1+2×C43⋊C3 | C32 | semidirect |
| 20. C32×C43⋊C9 | C32 | semidirect |
| 25. C3×C9×C43⋊C3 | C32 | semidirect |
| 26. #16812511 | C32 | semidirect |
| 27. #16812510 | C32 | semidirect |
| 28. #16812509 | C32 | semidirect |
| 29. C3×3−1+2×C43 | C32 | semidirect |
| 31. C32×C9×C43 | C32 | semidirect |
| 32. C43×#731 | C32 | semidirect |
| 42. #11923958 | C33 | semidirect |
| 51. C3×C43⋊C9 | C33 | semidirect |
| 58. 3−1+2×C43 | C33 | semidirect |
| 64. C3×C9×C43 | C33 | semidirect |
| 78. C3×C43⋊C3 | #731 | direct (N × H) |
| 92. C3×#731 | C43⋊C3 | direct (N × H) |
| 96. C3×C43 | C3×#731 | semidirect |
| 100. C43⋊C3 | C3×#731 | direct (N × H) |
| 108. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 120. C32×C9 | C3×C43⋊C3 | semidirect |
| 124. #731 | C3×C43⋊C3 | direct (N × H) |
| 125. C43 | C32×#731 | semidirect |
| 141. 3−1+2 | C32×C43⋊C3 | semidirect |
| 157. C3×C9 | C32×C43⋊C3 | semidirect |
| 183. C3 | #731×C43⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32×C9×C43⋊C3 | 3 |
| C3×#16812511 | 3 |
| C3×#16812510 | 3 |
| C3×#16812509 | 3 |
| #731×C43⋊C3 | 3 |
| C3×C43×#731 | 3 |
| C32×#731 | 43 |