Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×#15692280 | C2 | semidirect |
| 2. C22×#13108059 | C2 | semidirect |
| 3. #20265651 | C2 | semidirect |
| 4. #20265389 | C2 | semidirect |
| 5. #20265369 | C2 | semidirect |
| 6. #20265204 | C2 | semidirect |
| 7. #20265182 | C2 | semidirect |
| 8. #20265173 | C2 | semidirect |
| 9. #535×C101 | C2 | semidirect |
| 12. C2×#13108061 | C22 | semidirect |
| 15. C2×#13108059 | C22 | semidirect |
| 18. C4×D404 | C22 | semidirect |
| 22. C4⋊#11717579 | C22 | semidirect |
| 23. #15692179 | C22 | semidirect |
| 24. #15692176 | C22 | semidirect |
| 25. #15692176 | C22 | semidirect |
| 28. #127×C101 | C22 | semidirect |
| 29. #124×C101 | C22 | semidirect |
| 36. C2×D404 | D4 | semidirect |
| 122. C101 | #3041 | semidirect |
| 125. #535 | D101 | semidirect |
| 142. #127 | C2×D101 | semidirect |
| 143. #124 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692280 | 2 |
| C22×#13108059 | 2 |
| #20265651 | 2 |
| #20265389 | 2 |
| #20265369 | 2 |
| #20265204 | 2 |
| #20265182 | 2 |
| #20265173 | 2 |
| #535×C101 | 2 |
| #3041 | 101 |