Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 1. #20265711 | C2 | semidirect |
| 2. C2×C4×D404 | C2 | semidirect |
| 3. #20265508 | C2 | semidirect |
| 4. #20265491 | C2 | semidirect |
| 5. #20265478 | C2 | semidirect |
| 6. #20265393 | C2 | semidirect |
| 7. #20265330 | C2 | semidirect |
| 9. #20265290 | C2 | semidirect |
| 10. #20265279 | C2 | semidirect |
| 11. #432×C101 | C2 | semidirect |
| 17. #15692247 | C22 | semidirect |
| 18. #15692243 | C22 | semidirect |
| 22. C4×Dic202 | C22 | semidirect |
| 27. C4×D404 | C22 | semidirect |
| 32. #15692189 | C22 | semidirect |
| 33. #15692187 | C22 | semidirect |
| 34. #15692180 | C22 | semidirect |
| 37. #15692177 | C22 | semidirect |
| 39. C4⋊C8×C101 | C22 | semidirect |
| 42. #97×C101 | C22 | semidirect |
| 141. C101 | #3114 | semidirect |
| 152. #432 | D101 | semidirect |
| 176. C4⋊C8 | C2×D101 | semidirect |
| 183. #97 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265711 | 2 |
| C2×C4×D404 | 2 |
| #20265508 | 2 |
| #20265491 | 2 |
| #20265478 | 2 |
| #20265393 | 2 |
| #20265330 | 2 |
| #20265313 | 2 |
| #20265290 | 2 |
| #20265279 | 2 |
| #432×C101 | 2 |
| #3114 | 101 |