Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1118 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 286 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. #23782924 | C3 | semidirect |
| 2. C43⋊H(5,𝔽3) | C3 | semidirect |
| 3. C3×H(3,𝔽3)×C43⋊C3 | C3 | semidirect |
| 4. #23782883 | C3 | semidirect |
| 5. C3×#16812508 | C3 | semidirect |
| 6. C43×3−1+4 | C3 | semidirect |
| 7. C33×C43⋊C3 | C32 | semidirect |
| 9. C3×#11923958 | C32 | semidirect |
| 10. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 11. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 14. #16812508 | C32 | semidirect |
| 15. #16812508 | C32 | semidirect |
| 17. C3×3−1+2×C43 | C32 | semidirect |
| 49. 3−1+4 | C43⋊C3 | semidirect |
| 64. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 72. C43 | #10624930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782924 | 3 |
| C43⋊H(5,𝔽3) | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| #23782883 | 3 |
| C3×#16812508 | 3 |
| C43×3−1+4 | 3 |
| #10624930 | 43 |