Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#15692302 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. C22×#13108062 | C2 | semidirect |
| 4. #20265320 | C2 | semidirect |
| 5. #20265315 | C2 | semidirect |
| 6. #20265185 | C2 | semidirect |
| 7. #20265171 | C2 | semidirect |
| 8. #20265144 | C2 | semidirect |
| 9. #535×C101 | C2 | semidirect |
| 13. C2×#13108074 | C22 | semidirect |
| 17. C22×Dic202 | C22 | semidirect |
| 26. #15692178 | C22 | semidirect |
| 27. #15692178 | C22 | semidirect |
| 28. #15692175 | C22 | semidirect |
| 29. C22⋊#11717579 | C22 | semidirect |
| 40. #13108074 | D4 | semidirect |
| 48. C2×Dic202 | D4 | semidirect |
| 146. C101 | #3010 | semidirect |
| 150. #535 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| C2×#15692281 | 2 |
| C22×#13108062 | 2 |
| #20265320 | 2 |
| #20265315 | 2 |
| #20265185 | 2 |
| #20265171 | 2 |
| #20265144 | 2 |
| #535×C101 | 2 |
| #3010 | 101 |