Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
944 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 454 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. #23782792 | C3 | semidirect |
| 3. C9×#11923958 | C3 | semidirect |
| 4. #23782779 | C3 | semidirect |
| 7. C3×#11923958 | C9 | semidirect |
| 12. (C43⋊C9)⋊C9 | C32 | semidirect |
| 16. C9×C43⋊C9 | C32 | semidirect |
| 21. #11923958 | C3×C9 | semidirect |
| 22. #11923958 | C3×C9 | semidirect |
| 24. C3×C43⋊C9 | C3×C9 | semidirect |
| 77. C43 | #10624863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| #23782792 | 3 |
| C9×#11923958 | 3 |
| #23782779 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624863 | 43 |