Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1124 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 292 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×#11923958 | C3 | semidirect |
| 3. #23782809 | C3 | semidirect |
| 4. #23782808 | C3 | semidirect |
| 5. #23782795 | C3 | semidirect |
| 6. C32×3−1+2×C43 | C3 | semidirect |
| 10. C3×#11923958 | C32 | semidirect |
| 11. C3×#11923958 | C32 | semidirect |
| 15. C32×C43⋊C9 | C32 | semidirect |
| 16. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 20. C3×3−1+2×C43 | C32 | semidirect |
| 21. C32×C9×C43 | C32 | semidirect |
| 56. C32×3−1+2 | C43⋊C3 | semidirect |
| 75. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 80. C32×C9 | C3×C43⋊C3 | semidirect |
| 82. C43 | #10624881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| #23782809 | 3 |
| #23782808 | 3 |
| #23782795 | 3 |
| C32×3−1+2×C43 | 3 |
| #10624881 | 43 |