Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
218 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 52 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. #23782816 | C3 | semidirect |
| 2. #23782808 | C3 | semidirect |
| 3. C9×#11923958 | C3 | semidirect |
| 4. #23782699 | C3 | semidirect |
| 5. #23782699 | C3 | semidirect |
| 6. #23782696 | C3 | semidirect |
| 7. #23782692 | C3 | semidirect |
| 8. #23782692 | C3 | semidirect |
| 9. #23782690 | C3 | semidirect |
| 10. #23782689 | C3 | semidirect |
| 11. #23782689 | C3 | semidirect |
| 13. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 93. C9×H(3,𝔽3) | C43⋊C3 | semidirect |
| 135. C43 | #10624623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782816 | 3 |
| #23782808 | 3 |
| C9×#11923958 | 3 |
| #23782699 | 3 |
| #23782696 | 3 |
| #23782692 | 3 |
| #23782690 | 3 |
| #23782689 | 3 |
| #23782686 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| #10624623 | 43 |