Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
926 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 926 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. #23782792 | C3 | semidirect |
| 4. C9×#11923958 | C3 | semidirect |
| 7. #23782779 | C3 | semidirect |
| 8. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 10. #16812524 | C9 | semidirect |
| 27. #11923958 | C3×C9 | semidirect |
| 30. C3×C43⋊C9 | C3×C9 | semidirect |
| 87. C43 | #10624864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812524 | 3 |
| #23782792 | 3 |
| C9×#11923958 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| #23782779 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| #10624864 | 43 |