Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
200 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 200 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. #23782907 | C3 | semidirect |
| 2. #23782890 | C3 | semidirect |
| 3. #23782847 | C3 | semidirect |
| 4. #23782765 | C3 | semidirect |
| 5. #23782758 | C3 | semidirect |
| 6. #23782755 | C3 | semidirect |
| 7. #23782751 | C3 | semidirect |
| 8. #23782747 | C3 | semidirect |
| 9. C43×#6878 | C3 | semidirect |
| 14. #16812515 | C32 | semidirect |
| 17. #16812513 | C32 | semidirect |
| 22. #16812500 | C32 | semidirect |
| 23. C43×#733 | C32 | semidirect |
| 25. C92×C43 | C32 | semidirect |
| 67. #6878 | C43⋊C3 | semidirect |
| 80. #733 | C3×C43⋊C3 | semidirect |
| 90. C92 | C3×C43⋊C3 | semidirect |
| 91. C43 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782907 | 3 |
| #23782890 | 3 |
| #23782847 | 3 |
| #23782765 | 3 |
| #23782758 | 3 |
| #23782755 | 3 |
| #23782751 | 3 |
| #23782747 | 3 |
| C43×#6878 | 3 |
| #10624851 | 43 |