Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1166 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1166 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. C3×#16812526 | C3 | semidirect |
| 2. C33×C43⋊C9 | C3 | semidirect |
| 3. #23782809 | C3 | semidirect |
| 4. #23782805 | C3 | semidirect |
| 5. #23782804 | C3 | semidirect |
| 6. #23782798 | C3 | semidirect |
| 8. #23782783 | C3 | semidirect |
| 9. C43×#6891 | C3 | semidirect |
| 12. C3×#11923957 | C32 | semidirect |
| 13. C3×#11923956 | C32 | semidirect |
| 22. C3×C9×C43⋊C3 | C32 | semidirect |
| 24. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 38. C3×C43⋊C9 | H(3,𝔽3) | semidirect |
| 57. C32×C43 | #737 | semidirect |
| 73. #6891 | C43⋊C3 | semidirect |
| 99. C43 | #10624869 | semidirect |
| 130. 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 |
| C33×C43⋊C9 | 3 |
| #23782809 | 3 |
| #23782805 | 3 |
| #23782804 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| #23782783 | 3 |
| C43×#6891 | 3 |
| #10624869 | 43 |