Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20265975 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. #20265944 | C2 | semidirect |
| 4. #20265445 | C2 | semidirect |
| 5. #20265438 | C2 | semidirect |
| 6. #20265225 | C2 | semidirect |
| 7. #20265159 | C2 | semidirect |
| 8. C2×#15692172 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C101 | C2 | semidirect |
| 12. #15692285 | C22 | semidirect |
| 16. #15692280 | C22 | semidirect |
| 18. C2×#13108062 | C22 | semidirect |
| 19. C2×#13108059 | C22 | semidirect |
| 21. #15692262 | C22 | semidirect |
| 26. #15692190 | C22 | semidirect |
| 27. #15692173 | C22 | semidirect |
| 28. #15692172 | C22 | semidirect |
| 29. #15692171 | C22 | semidirect |
| 148. C101 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265975 | 2 |
| C2×#15692281 | 2 |
| #20265944 | 2 |
| #20265445 | 2 |
| #20265438 | 2 |
| #20265225 | 2 |
| #20265159 | 2 |
| C2×#15692172 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3068 | 101 |