Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
698 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 292 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. #23782845 | C3 | semidirect |
| 2. #23782838 | C3 | semidirect |
| 3. #23782824 | C3 | semidirect |
| 4. #23782815 | C3 | semidirect |
| 5. #23782812 | C3 | semidirect |
| 7. #23782782 | C3 | semidirect |
| 8. #23782782 | C3 | semidirect |
| 9. C3×#16812499 | C3 | semidirect |
| 48. C3×C9×C43 | 3−1+2 | semidirect |
| 105. C43 | #10624887 | semidirect |
| 119. C3×C9 | #11923958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782845 | 3 |
| #23782838 | 3 |
| #23782824 | 3 |
| #23782815 | 3 |
| #23782812 | 3 |
| #23782800 | 3 |
| #23782782 | 3 |
| C3×#16812499 | 3 |
| C3×C43×#737 | 3 |
| #10624887 | 43 |