Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
356 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 5. #23782699 | C3 | semidirect |
| 6. #23782699 | C3 | semidirect |
| 7. #23782698 | C3 | semidirect |
| 8. #23782698 | C3 | semidirect |
| 9. C43×#6860 | C3 | semidirect |
| 92. #6860 | C43⋊C3 | semidirect |
| 123. C43 | #10624594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| #23782797 | 3 |
| #23782795 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782699 | 3 |
| #23782698 | 3 |
| C43×#6860 | 3 |
| #10624594 | 43 |