Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1244 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 316 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×#11923956 | C3 | semidirect |
| 3. #23782804 | C3 | semidirect |
| 4. #23782803 | C3 | semidirect |
| 5. #23782796 | C3 | semidirect |
| 6. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 7. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 12. C3×#11923956 | C32 | semidirect |
| 13. C3×#11923956 | C32 | semidirect |
| 16. C32×C43⋊C9 | C32 | semidirect |
| 17. C32⋊(C43⋊C9) | C32 | semidirect |
| 18. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 20. C32×C9×C43 | C32 | semidirect |
| 21. C43×C32⋊C9 | C32 | semidirect |
| 30. #11923956 | H(3,𝔽3) | direct (N × H) |
| 36. H(3,𝔽3)×C43 | 3−1+2 | semidirect |
| 43. C32×C43 | C3×3−1+2 | semidirect |
| 53. C9×C43 | C3×H(3,𝔽3) | semidirect |
| 55. C43⋊C9 | C3×H(3,𝔽3) | semidirect |
| 62. C9×H(3,𝔽3) | C43⋊C3 | semidirect |
| 79. C32×C9 | C3×C43⋊C3 | semidirect |
| 82. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 83. C43 | H(3,𝔽3)×3−1+2 | semidirect |
| 95. H(3,𝔽3) | #11923956 | direct (N × H) |
| 111. C32 | C3×#11923956 | semidirect |
| 116. C9 | H(3,𝔽3)×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923956 | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| #23782804 | 3 |
| #23782803 | 3 |
| #23782796 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| H(3,𝔽3)×3−1+2 | 43 |