Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1148 conjugacy classes of subgroups; only the 508 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 508 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 |
|---|---|---|
| 3. #23782792 | C3 | direct (N × H) |
| 4. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×C9×C43⋊C9 | C3 | semidirect |
| 8. C3×#11923958 | C9 | semidirect |
| 16. (C43⋊C9)⋊C9 | C32 | semidirect |
| 18. C9×C43⋊C9 | C32 | semidirect |
| 22. #11923958 | C3×C9 | semidirect |
| 26. C3×C43⋊C9 | C3×C9 | semidirect |
| 27. C3×C43⋊C9 | 3−1+2 | semidirect |
| 54. C43⋊C9 | C32×C9 | semidirect |
| 55. C43⋊C9 | C3×3−1+2 | semidirect |
| 64. C3×C43 | C9×3−1+2 | semidirect |
| 83. C43 | C3×C9×3−1+2 | semidirect |
| 118. C3 | #23782792 | 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 |
| C33×C43⋊C9 | 3 |
| #23782792 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×C9×C43⋊C9 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C3×C9×3−1+2 | 43 |