Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1082 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 298 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. C3×#16812526 | C3 | semidirect |
| 2. #23782809 | C3 | semidirect |
| 3. #23782803 | C3 | semidirect |
| 4. #23782802 | C3 | semidirect |
| 5. #23782799 | C3 | semidirect |
| 6. #23782798 | C3 | semidirect |
| 8. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 9. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 10. C32×3−1+2×C43 | C3 | semidirect |
| 13. C3×#11923957 | C32 | semidirect |
| 14. C3×#11923956 | C32 | semidirect |
| 19. C3×C9×C43⋊C3 | C32 | semidirect |
| 26. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 27. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 28. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 56. 3−1+2×C43 | H(3,𝔽3) | semidirect |
| 71. C32×C43 | #737 | semidirect |
| 83. C32×3−1+2 | C43⋊C3 | semidirect |
| 123. C43 | #10624896 | semidirect |
| 136. 3−1+2 | C32⋊(C43⋊C3) | semidirect |
| 162. C32 | #16812526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812526 | 3 |
| #23782809 | 3 |
| #23782803 | 3 |
| #23782802 | 3 |
| #23782799 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C32×3−1+2×C43 | 3 |
| #10624896 | 43 |