Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782817 | C3 | semidirect |
| 2. #23782809 | C3 | semidirect |
| 3. 3−1+2×C43⋊C9 | C3 | semidirect |
| 4. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 5. #23782698 | C3 | semidirect |
| 6. #23782698 | C3 | semidirect |
| 7. #23782697 | C3 | semidirect |
| 8. #23782694 | C3 | semidirect |
| 9. #23782691 | C3 | semidirect |
| 10. #23782689 | C3 | semidirect |
| 11. #23782688 | C3 | semidirect |
| 13. C43×#6857 | C3 | semidirect |
| 101. #6857 | C43⋊C3 | semidirect |
| 135. C43 | #10624623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782817 | 3 |
| #23782809 | 3 |
| 3−1+2×C43⋊C9 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| #23782698 | 3 |
| #23782697 | 3 |
| #23782694 | 3 |
| #23782691 | 3 |
| #23782689 | 3 |
| #23782688 | 3 |
| #23782686 | 3 |
| C43×#6857 | 3 |
| #10624623 | 43 |