Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
986 conjugacy classes of subgroups; only the 472 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 472 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. C9×#11923956 | C3 | semidirect |
| 3. C9×#11923957 | C3 | semidirect |
| 4. C9×#11923958 | C3 | semidirect |
| 6. #23782782 | C3 | semidirect |
| 7. #23782780 | C3 | semidirect |
| 8. C92×C43⋊C3 | C3 | semidirect |
| 9. C3×C92×C43 | C3 | semidirect |
| 10. #16812525 | C9 | direct (N × H) |
| 31. #11923958 | C3×C9 | semidirect |
| 32. #11923957 | C3×C9 | semidirect |
| 33. #11923956 | C3×C9 | semidirect |
| 38. C9×C43⋊C3 | C3×C9 | semidirect |
| 41. C3×C9×C43 | C3×C9 | semidirect |
| 57. C9×C43 | #737 | semidirect |
| 68. C3×C92 | C43⋊C3 | semidirect |
| 93. C43 | C9×#737 | semidirect |
| 105. C3×C9 | C9×C43⋊C3 | semidirect |
| 122. C9 | #16812525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| C9×#11923956 | 3 |
| C9×#11923957 | 3 |
| C9×#11923958 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| #23782782 | 3 |
| #23782780 | 3 |
| C92×C43⋊C3 | 3 |
| C3×C92×C43 | 3 |
| C9×#737 | 43 |