Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
164 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 7. #16812505 | C9 | semidirect |
| 12. C3×C43⋊C27 | C9 | semidirect |
| 20. C43×C27⋊C3 | C9 | semidirect |
| 70. C27⋊C3 | C43⋊C9 | semidirect |
| 81. C43 | #10624468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812505 | 3 |
| C32×C43⋊C27 | 3 |
| #23782782 | 3 |
| C3×C43×C27⋊C3 | 3 |
| #10624468 | 43 |