Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
2150 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 2150 conjugacy classes of subgroups — too many to draw. Only its 202 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. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 3. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 4. C3×C43×C32⋊C9 | C3 | semidirect |
| 10. C33×C43⋊C3 | C9 | semidirect |
| 12. C32×C43⋊C9 | C32 | semidirect |
| 16. C32×C9×C43 | C32 | semidirect |
| 50. C32×C43 | C32⋊C9 | semidirect |
| 66. C3×C43⋊C3 | C32⋊C9 | semidirect |
| 72. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 90. C32×C9 | C3×C43⋊C3 | semidirect |
| 94. C43 | #10624547 | semidirect |
| 136. C32 | (C3×C43⋊C3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C43⋊C3 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624547 | 43 |