Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #20266013 | C2 | semidirect |
| 2. C2×#15692302 | C2 | semidirect |
| 3. #20265994 | C2 | semidirect |
| 4. #20265989 | C2 | semidirect |
| 5. #20265977 | C2 | semidirect |
| 6. C2×#15692288 | C2 | semidirect |
| 7. #568×C101 | C2 | semidirect |
| 10. #15692302 | C22 | semidirect |
| 11. #15692302 | C22 | semidirect |
| 12. #15692301 | C22 | semidirect |
| 15. C2×#13108074 | C22 | semidirect |
| 18. C22×Dic202 | C22 | semidirect |
| 20. #15692288 | C22 | semidirect |
| 21. #15692288 | C22 | semidirect |
| 22. #15692288 | C22 | semidirect |
| 23. #15692283 | C22 | semidirect |
| 24. #15692283 | C22 | semidirect |
| 25. #15692277 | C22 | semidirect |
| 26. C2×Dic404 | C22 | semidirect |
| 27. C2×#13108063 | C22 | semidirect |
| 29. #131×C101 | C22 | semidirect |
| 30. C2×M16×C101 | C22 | semidirect |
| 113. C101 | #3586 | semidirect |
| 120. #568 | D101 | semidirect |
| 142. #131 | C2×D101 | semidirect |
| 143. C2×M16 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| C2×#15692302 | 2 |
| #20265994 | 2 |
| #20265989 | 2 |
| #20265977 | 2 |
| C2×#15692288 | 2 |
| #568×C101 | 2 |
| #3586 | 101 |