Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #20265658 | C2 | semidirect |
| 3. #20265504 | C2 | semidirect |
| 4. #20265503 | C2 | semidirect |
| 5. #20265497 | C2 | semidirect |
| 6. #20265492 | C2 | semidirect |
| 7. #20265213 | C2 | semidirect |
| 8. #20265183 | C2 | semidirect |
| 9. C2×#15692175 | C2 | semidirect |
| 10. #20265145 | C2 | semidirect |
| 11. #428×C101 | C2 | semidirect |
| 24. #15692213 | C22 | semidirect |
| 25. C4⋊C4×D101 | C22 | semidirect |
| 26. #15692188 | C22 | semidirect |
| 27. #15692188 | C22 | semidirect |
| 28. #15692186 | C22 | semidirect |
| 29. #15692186 | C22 | semidirect |
| 34. #15692167 | C22 | semidirect |
| 35. #15692167 | C22 | semidirect |
| 39. #107×C101 | C22 | semidirect |
| 40. #106×C101 | C22 | semidirect |
| 135. C101 | #3096 | semidirect |
| 142. #428 | D101 | semidirect |
| 166. #107 | C2×D101 | semidirect |
| 169. #106 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265746 | 2 |
| #20265658 | 2 |
| #20265504 | 2 |
| #20265503 | 2 |
| #20265497 | 2 |
| #20265492 | 2 |
| #20265213 | 2 |
| #20265183 | 2 |
| C2×#15692175 | 2 |
| #20265145 | 2 |
| #428×C101 | 2 |
| #3096 | 101 |