Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
374 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 13. #16812500 | C9 | semidirect |
| 44. C9×C43 | C9⋊C9 | semidirect |
| 72. C43 | #10624561 | semidirect |
| 102. C9 | (C43⋊C9)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812500 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C43⋊#6855 | 3 |
| C3×C92×C43 | 3 |
| #10624561 | 43 |