Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #20265808 | C2 | semidirect |
| 3. #20265480 | C2 | semidirect |
| 4. #20265476 | C2 | semidirect |
| 5. #20265466 | C2 | semidirect |
| 6. #20265456 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265205 | C2 | semidirect |
| 11. #428×C101 | C2 | semidirect |
| 15. #15692254 | C22 | semidirect |
| 17. #15692246 | C22 | semidirect |
| 26. #15692188 | C22 | semidirect |
| 27. #15692188 | C22 | semidirect |
| 28. #15692186 | C22 | semidirect |
| 29. #15692186 | C22 | semidirect |
| 30. #15692184 | C22 | semidirect |
| 31. #15692184 | C22 | semidirect |
| 39. #107×C101 | C22 | semidirect |
| 40. #106×C101 | C22 | semidirect |
| 45. C2×D404 | Q8 | semidirect |
| 125. C101 | #3081 | semidirect |
| 132. #428 | D101 | semidirect |
| 156. #107 | C2×D101 | semidirect |
| 159. #106 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265808 | 2 |
| #20265651 | 2 |
| #20265480 | 2 |
| #20265476 | 2 |
| #20265466 | 2 |
| #20265456 | 2 |
| #20265213 | 2 |
| #20265205 | 2 |
| #20265183 | 2 |
| C2×#15692175 | 2 |
| #428×C101 | 2 |
| #3081 | 101 |