Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
432 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 64 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. C33×C43⋊C9 | C3 | semidirect |
| 3. #23782818 | C3 | semidirect |
| 4. #23782805 | C3 | semidirect |
| 5. #23782725 | C3 | semidirect |
| 6. #23782722 | C3 | semidirect |
| 7. #23782719 | C3 | semidirect |
| 8. #23782712 | C3 | semidirect |
| 9. C43×#6866 | C3 | semidirect |
| 48. C33×C43 | 3−1+2 | semidirect |
| 73. C43⋊C9 | AΣL(1,𝔽27) | semidirect |
| 82. #6866 | C43⋊C3 | semidirect |
| 108. C43 | #10624784 | semidirect |
| 114. C33 | #11923957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C43⋊C9 | 3 |
| C3×#16812507 | 3 |
| #23782818 | 3 |
| #23782805 | 3 |
| #23782725 | 3 |
| #23782722 | 3 |
| #23782719 | 3 |
| #23782712 | 3 |
| C43×#6866 | 3 |
| #10624784 | 43 |