Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1076 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1076 conjugacy classes of subgroups — too many to draw. Only its 382 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. #23782845 | C3 | direct (N × H) |
| 3. C3×#16812500 | C3 | semidirect |
| 4. C3×#16812499 | C3 | semidirect |
| 5. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×C9×C43⋊C9 | C3 | semidirect |
| 13. #16812500 | C32 | semidirect |
| 14. #16812499 | C32 | semidirect |
| 15. (C43⋊C9)⋊C9 | C32 | semidirect |
| 16. C9×C43⋊C9 | C32 | semidirect |
| 25. C3×C43⋊C9 | 3−1+2 | semidirect |
| 35. C3×C9×C43 | 3−1+2 | semidirect |
| 46. C9×C43 | C3×3−1+2 | semidirect |
| 49. C43⋊C9 | C3×3−1+2 | semidirect |
| 58. C3×C43 | #6900 | semidirect |
| 75. C43 | C3×#6900 | semidirect |
| 89. C3×C9 | #11923958 | semidirect |
| 102. C9 | C3×#11923958 | semidirect |
| 104. C3 | #23782845 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| #23782845 | 3 |
| C3×#16812500 | 3 |
| C3×#16812499 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C3×C9×C43⋊C9 | 3 |
| C32×3−1+2×C43 | 3 |
| C3×#6900 | 43 |