Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1304 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1304 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×C32⋊(C43⋊C3) | C3 | semidirect |
| 2. #23782892 | C3 | direct (N × H) |
| 3. C3×#16812513 | C3 | semidirect |
| 4. C32×3−1+2×C43 | C3 | semidirect |
| 8. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 9. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 10. #16812513 | C32 | semidirect |
| 14. C3×3−1+2×C43 | C32 | semidirect |
| 15. C32×C9×C43 | C32 | semidirect |
| 21. C32⋊(C43⋊C3) | C33 | semidirect |
| 30. C3×C9×C43 | C33 | semidirect |
| 44. C32×3−1+2 | C43⋊C3 | semidirect |
| 51. C3×C43 | #6911 | semidirect |
| 58. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 63. C32×C9 | C3×C43⋊C3 | semidirect |
| 65. C43 | C3×#6911 | semidirect |
| 80. C3×C9 | C32×C43⋊C3 | semidirect |
| 97. C3 | #23782892 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C43⋊C3) | 3 |
| #23782892 | 3 |
| C3×#16812513 | 3 |
| C32×3−1+2×C43 | 3 |
| C3×#6911 | 43 |