Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20265660 | C2 | semidirect |
| 2. #20265498 | C2 | semidirect |
| 3. #20265498 | C2 | semidirect |
| 4. #20265493 | C2 | semidirect |
| 5. #20265488 | C2 | semidirect |
| 6. #20265220 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265182 | C2 | semidirect |
| 9. C2×#15692176 | C2 | semidirect |
| 10. #20265144 | C2 | semidirect |
| 18. #15692214 | C22 | semidirect |
| 20. C2×C4⋊Dic101 | C22 | semidirect |
| 21. #15692188 | C22 | semidirect |
| 22. #15692188 | C22 | semidirect |
| 23. #15692188 | C22 | semidirect |
| 24. #15692186 | C22 | semidirect |
| 25. #15692186 | C22 | semidirect |
| 26. #15692186 | C22 | semidirect |
| 31. C22⋊#11717579 | C22 | semidirect |
| 32. C22⋊#11717579 | C22 | semidirect |
| 135. C101 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265660 | 2 |
| #20265498 | 2 |
| #20265493 | 2 |
| #20265488 | 2 |
| #20265220 | 2 |
| #20265213 | 2 |
| #20265182 | 2 |
| C2×#15692176 | 2 |
| #20265144 | 2 |
| #535×C101 | 2 |
| #3096 | 101 |