Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20265977 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. C2×#15692281 | C2 | semidirect |
| 4. #20265943 | C2 | semidirect |
| 5. #20265446 | C2 | semidirect |
| 6. #20265439 | C2 | semidirect |
| 7. #20265225 | C2 | semidirect |
| 8. #20265159 | C2 | semidirect |
| 9. C2×#100×C101 | C2 | semidirect |
| 13. #15692288 | C22 | semidirect |
| 15. #15692283 | C22 | semidirect |
| 22. C2×#13108062 | C22 | semidirect |
| 24. C2×#13108059 | C22 | semidirect |
| 25. #15692263 | C22 | semidirect |
| 30. #15692190 | C22 | semidirect |
| 31. #15692173 | C22 | semidirect |
| 32. #15692171 | C22 | semidirect |
| 36. #100×C101 | C22 | semidirect |
| 148. C101 | #3068 | semidirect |
| 157. C2×#100 | D101 | semidirect |
| 184. #100 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| C2×#15692281 | 2 |
| #20265943 | 2 |
| #20265446 | 2 |
| #20265439 | 2 |
| #20265225 | 2 |
| #20265159 | 2 |
| C2×#100×C101 | 2 |
| #3068 | 101 |