Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
476 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 58 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. #23782797 | C3 | semidirect |
| 3. #23782796 | C3 | semidirect |
| 4. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 5. #23782712 | C3 | semidirect |
| 6. #23782711 | C3 | semidirect |
| 7. #23782711 | C3 | semidirect |
| 8. #23782711 | C3 | semidirect |
| 9. C43×#6866 | C3 | semidirect |
| 112. #6866 | C43⋊C3 | semidirect |
| 146. C43 | #10624805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C43⋊C3) | 3 |
| #23782797 | 3 |
| #23782796 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782712 | 3 |
| #23782711 | 3 |
| C43×#6866 | 3 |
| #10624805 | 43 |