Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
458 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C32×#11923957 | C3 | semidirect |
| 2. C3×#16812514 | C3 | semidirect |
| 3. C3×#16812512 | C3 | semidirect |
| 4. C3×#16812510 | C3 | semidirect |
| 5. C3×#16812508 | C3 | semidirect |
| 6. C3×#16812506 | C3 | semidirect |
| 7. #23782809 | C3 | semidirect |
| 8. #23782806 | C3 | semidirect |
| 9. C3×C43×#731 | C3 | semidirect |
| 95. C3×#731 | C43⋊C3 | semidirect |
| 129. C43 | #10624739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923957 | 3 |
| C3×#16812514 | 3 |
| C3×#16812512 | 3 |
| C3×#16812510 | 3 |
| C3×#16812508 | 3 |
| C3×#16812506 | 3 |
| #23782809 | 3 |
| #23782806 | 3 |
| C3×C43×#731 | 3 |
| #10624739 | 43 |