Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261442 | C2 | semidirect |
| 2. #20261081 | C2 | semidirect |
| 3. #20261051 | C2 | semidirect |
| 4. #20261025 | C2 | semidirect |
| 5. #20260962 | C2 | semidirect |
| 6. #20260932 | C2 | semidirect |
| 7. #20260886 | C2 | semidirect |
| 8. C4×#13095499 | C2 | semidirect |
| 9. D4×#11715895 | C2 | semidirect |
| 10. C2×#15690731 | C2 | semidirect |
| 13. C2×#13095499 | C22 | semidirect |
| 14. C22×#11715895 | C22 | semidirect |
| 15. #15690810 | C22 | semidirect |
| 17. #15690789 | C22 | semidirect |
| 19. C4×Dic194 | C22 | semidirect |
| 21. C2×C4⋊Dic97 | C22 | semidirect |
| 22. #15690741 | C22 | semidirect |
| 23. #15690741 | C22 | semidirect |
| 24. C4⋊#11715895 | C22 | semidirect |
| 25. #15690733 | C22 | semidirect |
| 28. #15690731 | C22 | semidirect |
| 29. #15690731 | C22 | semidirect |
| 30. #15690731 | C22 | semidirect |
| 31. C22⋊#11715895 | C22 | semidirect |
| 32. C4×#11715895 | C22 | semidirect |
| 90. D4×C97 | SD16 | semidirect |
| 137. C97 | #3295 | semidirect |
| 230. D4 | #13095499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261442 | 2 |
| #20261081 | 2 |
| #20261051 | 2 |
| #20261025 | 2 |
| #20260962 | 2 |
| #20260932 | 2 |
| #20260886 | 2 |
| C4×#13095499 | 2 |
| D4×#11715895 | 2 |
| C2×#15690731 | 2 |
| D42×C97 | 2 |
| #3295 | 97 |