Finite Group DatabasebetaFinite Group Databasebeta← 3−1+2×C32⋊(C43⋊C3) #44534951
Order 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. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 3. #23782803 | C3 | semidirect |
| 4. #23782802 | C3 | semidirect |
| 5. #23782799 | C3 | semidirect |
| 6. #23782798 | C3 | semidirect |
| 7. #23782795 | C3 | semidirect |
| 8. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 9. C32×3−1+2×C43 | C3 | semidirect |
| 12. C3×#11923957 | C32 | semidirect |
| 13. C3×#11923956 | C32 | semidirect |
| 20. C3×C9×C43⋊C3 | C32 | semidirect |
| 21. C32⋊(C43⋊C9) | C32 | semidirect |
| 22. C32⋊(C43⋊C9) | C32 | semidirect |
| 23. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 24. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 25. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 30. C3×3−1+2×C43 | C32 | semidirect |
| 31. C32×C9×C43 | C32 | semidirect |
| 44. C32⋊(C43⋊C3) | 3−1+2 | direct (N × H) |
| 55. 3−1+2×C43 | H(3,𝔽3) | semidirect |
| 69. C32×C43 | C3×3−1+2 | semidirect |
| 80. C3×C43⋊C3 | C3×3−1+2 | semidirect |
| 82. C9×C43 | C3×H(3,𝔽3) | semidirect |
| 85. C32×3−1+2 | C43⋊C3 | semidirect |
| 111. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 118. C32×C9 | C3×C43⋊C3 | semidirect |
| 124. C43 | H(3,𝔽3)×3−1+2 | semidirect |
| 142. 3−1+2 | C32⋊(C43⋊C3) | direct (N × H) |
| 171. C32 | 3−1+2×C43⋊C3 | semidirect |
| 175. C9 | C3×C32⋊(C43⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| #23782803 | 3 |
| #23782802 | 3 |
| #23782799 | 3 |
| #23782798 | 3 |
| #23782795 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C32×3−1+2×C43 | 3 |
| H(3,𝔽3)×3−1+2 | 43 |