Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
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. #20265884 | C2 | semidirect |
| 2. #20265523 | C2 | semidirect |
| 3. #20265493 | C2 | semidirect |
| 4. #20265467 | C2 | semidirect |
| 5. #20265404 | C2 | semidirect |
| 6. #20265374 | C2 | semidirect |
| 7. #20265328 | C2 | semidirect |
| 8. C4×#13108062 | C2 | semidirect |
| 9. D4×#11717579 | C2 | semidirect |
| 10. C2×#15692176 | C2 | semidirect |
| 13. C2×#13108062 | C22 | semidirect |
| 14. C22×#11717579 | C22 | semidirect |
| 15. #15692255 | C22 | semidirect |
| 17. #15692234 | C22 | semidirect |
| 19. C4×Dic202 | C22 | semidirect |
| 21. C2×C4⋊Dic101 | C22 | semidirect |
| 22. #15692186 | C22 | semidirect |
| 23. #15692186 | C22 | semidirect |
| 24. C4⋊#11717579 | C22 | semidirect |
| 25. #15692178 | C22 | semidirect |
| 28. #15692176 | C22 | semidirect |
| 29. #15692176 | C22 | semidirect |
| 30. #15692176 | C22 | semidirect |
| 31. C22⋊#11717579 | C22 | semidirect |
| 32. C4×#11717579 | C22 | semidirect |
| 90. D4×C101 | SD16 | semidirect |
| 137. C101 | #3295 | semidirect |
| 230. D4 | #13108062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265884 | 2 |
| #20265523 | 2 |
| #20265493 | 2 |
| #20265467 | 2 |
| #20265404 | 2 |
| #20265374 | 2 |
| #20265328 | 2 |
| C4×#13108062 | 2 |
| D4×#11717579 | 2 |
| C2×#15692176 | 2 |
| D42×C101 | 2 |
| #3295 | 101 |