Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 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. #23782822 | C3 | semidirect |
| 2. #23782782 | C3 | semidirect |
| 4. #23782715 | C3 | semidirect |
| 5. #23782715 | C3 | semidirect |
| 6. #23782715 | C3 | semidirect |
| 7. #23782713 | C3 | semidirect |
| 8. #23782713 | C3 | semidirect |
| 9. #23782713 | C3 | semidirect |
| 13. C43×#6895 | C3 | semidirect |
| 88. #6895 | C43⋊C3 | semidirect |
| 131. C43 | #10624810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782822 | 3 |
| #23782782 | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| #23782715 | 3 |
| #23782713 | 3 |
| #23782711 | 3 |
| C43×#6895 | 3 |
| #10624810 | 43 |