Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
200 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 4. #23782764 | C3 | semidirect |
| 5. #23782763 | C3 | semidirect |
| 6. #23782762 | C3 | semidirect |
| 7. #23782761 | C3 | semidirect |
| 8. #23782760 | C3 | semidirect |
| 9. C43×#6882 | C3 | semidirect |
| 70. #6882 | C43⋊C3 | direct (N × H) |
| 75. C43⋊C3 | #6882 | direct (N × H) |
| 91. C43 | C3×#6882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C43⋊C3 | 3 |
| C9⋊C9×C43⋊C3 | 3 |
| #23782764 | 3 |
| #23782763 | 3 |
| #23782762 | 3 |
| #23782761 | 3 |
| #23782760 | 3 |
| C43×#6882 | 3 |
| C3×#6882 | 43 |