Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 274 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×#16812526 | C3 | semidirect |
| 2. C32×#11923957 | C3 | semidirect |
| 3. #23782906 | C3 | direct (N × H) |
| 4. C3×#16812515 | C3 | semidirect |
| 5. C3×#16812513 | C3 | semidirect |
| 6. C3×#16812511 | C3 | semidirect |
| 7. C3×#16812508 | C3 | semidirect |
| 8. C3×C43×#733 | C3 | semidirect |
| 11. #16812526 | C32 | semidirect |
| 16. C3×#11923957 | C32 | semidirect |
| 22. #16812515 | C32 | semidirect |
| 23. #16812513 | C32 | semidirect |
| 24. #16812511 | C32 | semidirect |
| 25. #16812508 | C32 | semidirect |
| 28. C43×#733 | C32 | semidirect |
| 76. C3×#733 | C43⋊C3 | semidirect |
| 82. C3×C43 | #6913 | semidirect |
| 102. #733 | C3×C43⋊C3 | semidirect |
| 106. C43 | C3×#6913 | semidirect |
| 153. C3 | #23782906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812526 | 3 |
| C32×#11923957 | 3 |
| #23782906 | 3 |
| C3×#16812515 | 3 |
| C3×#16812513 | 3 |
| C3×#16812511 | 3 |
| C3×#16812508 | 3 |
| C3×C43×#733 | 3 |
| C3×#6913 | 43 |