Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
456 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 61 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. C43⋊H(5,𝔽3) | C3 | semidirect |
| 2. #23782888 | C3 | semidirect |
| 3. #23782887 | C3 | semidirect |
| 4. #23782883 | C3 | semidirect |
| 5. #23782883 | C3 | semidirect |
| 6. #23782882 | C3 | semidirect |
| 7. #23782882 | C3 | semidirect |
| 8. #23782881 | C3 | semidirect |
| 9. C3×#16812512 | C3 | semidirect |
| 10. C3×#16812511 | C3 | semidirect |
| 11. #23782809 | C3 | semidirect |
| 12. #23782806 | C3 | semidirect |
| 13. C43×#6909 | C3 | semidirect |
| 14. C3×#11923958 | C32 | semidirect |
| 15. C3×#11923958 | C32 | semidirect |
| 16. C3×#11923958 | C32 | semidirect |
| 17. C3×#11923958 | C32 | semidirect |
| 22. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 26. C32×C43⋊C9 | C32 | semidirect |
| 38. C3×3−1+2×C43 | C32 | semidirect |
| 39. C3×3−1+2×C43 | C32 | semidirect |
| 41. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 132. #6909 | C43⋊C3 | semidirect |
| 152. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 153. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 163. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 177. C43 | #10624748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43⋊H(5,𝔽3) | 3 |
| #23782888 | 3 |
| #23782887 | 3 |
| #23782883 | 3 |
| #23782882 | 3 |
| #23782881 | 3 |
| C3×#16812512 | 3 |
| C3×#16812511 | 3 |
| #23782809 | 3 |
| #23782806 | 3 |
| C43×#6909 | 3 |
| #10624748 | 43 |