Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
432 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. #23782815 | C3 | semidirect |
| 3. #23782802 | C3 | semidirect |
| 4. #23782724 | C3 | semidirect |
| 5. #23782721 | C3 | semidirect |
| 6. #23782712 | C3 | semidirect |
| 7. C33×C9×C43 | C3 | semidirect |
| 36. C33×C43 | 3−1+2 | semidirect |
| 61. C9×C43 | AΣL(1,𝔽27) | semidirect |
| 65. C33×C9 | C43⋊C3 | semidirect |
| 94. C43 | #10624784 | semidirect |
| 100. C33 | #11923957 | semidirect |
| 135. C9 | #16812507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812507 | 3 |
| #23782815 | 3 |
| #23782802 | 3 |
| #23782724 | 3 |
| #23782721 | 3 |
| #23782712 | 3 |
| C33×C9×C43 | 3 |
| #10624784 | 43 |