Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
188 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 1. #23782902 | C3 | semidirect |
| 2. #23782894 | C3 | semidirect |
| 3. #23782848 | C3 | semidirect |
| 4. #23782769 | C3 | semidirect |
| 5. #23782764 | C3 | semidirect |
| 6. #23782762 | C3 | semidirect |
| 7. #23782753 | C3 | semidirect |
| 8. #23782745 | C3 | semidirect |
| 9. C43×#6881 | C3 | semidirect |
| 64. #6881 | C43⋊C3 | semidirect |
| 87. C43 | #10624852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782902 | 3 |
| #23782894 | 3 |
| #23782848 | 3 |
| #23782769 | 3 |
| #23782764 | 3 |
| #23782762 | 3 |
| #23782753 | 3 |
| #23782745 | 3 |
| C43×#6881 | 3 |
| #10624852 | 43 |