Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
716 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. #23782848 | C3 | semidirect |
| 3. #23782847 | C3 | semidirect |
| 4. #23782844 | C3 | semidirect |
| 5. #23782839 | C3 | semidirect |
| 6. #23782819 | C3 | semidirect |
| 8. #23782782 | C3 | semidirect |
| 9. C43×#6887 | C3 | semidirect |
| 18. #16812500 | C32 | semidirect |
| 19. #16812500 | C32 | semidirect |
| 20. #16812499 | C32 | semidirect |
| 21. (C43⋊C9)⋊C9 | C32 | semidirect |
| 24. C9×C43⋊C9 | C32 | semidirect |
| 26. C43×C9⋊C9 | C32 | semidirect |
| 28. C92×C43 | C32 | semidirect |
| 43. C3×C9×C43 | 3−1+2 | semidirect |
| 70. #6887 | C43⋊C3 | semidirect |
| 89. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 94. C92 | C3×C43⋊C3 | semidirect |
| 95. C43 | #10624884 | semidirect |
| 110. C3×C9 | #11923956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923956 | 3 |
| #23782848 | 3 |
| #23782847 | 3 |
| #23782844 | 3 |
| #23782839 | 3 |
| #23782819 | 3 |
| #23782796 | 3 |
| #23782782 | 3 |
| C43×#6887 | 3 |
| #10624884 | 43 |