Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 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. C22×#13108059 | C2 | semidirect |
| 2. C2×#15692263 | C2 | semidirect |
| 3. #20265746 | C2 | semidirect |
| 4. #20265744 | C2 | semidirect |
| 5. #20265429 | C2 | semidirect |
| 6. #20265412 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265183 | C2 | semidirect |
| 9. #418×C101 | C2 | semidirect |
| 16. C2×#13108057 | C22 | semidirect |
| 18. C2×C8×D101 | C22 | semidirect |
| 23. #15692230 | C22 | semidirect |
| 24. #15692226 | C22 | semidirect |
| 28. #15692188 | C22 | semidirect |
| 29. #15692186 | C22 | semidirect |
| 30. #15692177 | C22 | semidirect |
| 34. #102×C101 | C22 | semidirect |
| 51. C2×#11717579 | D4 | semidirect |
| 126. C101 | #3058 | semidirect |
| 135. #418 | D101 | semidirect |
| 160. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108059 | 2 |
| C2×#15692263 | 2 |
| #20265746 | 2 |
| #20265744 | 2 |
| #20265429 | 2 |
| #20265412 | 2 |
| #20265213 | 2 |
| #20265183 | 2 |
| #418×C101 | 2 |
| #3058 | 101 |