Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#15692281 | C2 | semidirect |
| 2. C2×#15692261 | C2 | semidirect |
| 3. #20265758 | C2 | semidirect |
| 4. #20265744 | C2 | semidirect |
| 5. #20265429 | C2 | semidirect |
| 6. #20265422 | C2 | semidirect |
| 7. #20265412 | C2 | semidirect |
| 8. #20265405 | C2 | semidirect |
| 9. #20265217 | C2 | semidirect |
| 10. #20265174 | C2 | semidirect |
| 11. C2×#102×C101 | C2 | semidirect |
| 19. C2×#13108057 | C22 | semidirect |
| 20. C2×C8×D101 | C22 | semidirect |
| 24. #15692235 | C22 | semidirect |
| 26. #15692230 | C22 | semidirect |
| 32. #15692188 | C22 | semidirect |
| 33. #15692186 | C22 | semidirect |
| 34. #15692180 | C22 | semidirect |
| 35. #15692180 | C22 | semidirect |
| 36. #15692177 | C22 | semidirect |
| 37. #15692177 | C22 | semidirect |
| 60. #13108058 | D4 | semidirect |
| 152. C101 | #3062 | semidirect |
| 163. C2×#102 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| C2×#15692261 | 2 |
| #20265758 | 2 |
| #20265744 | 2 |
| #20265429 | 2 |
| #20265422 | 2 |
| #20265412 | 2 |
| #20265405 | 2 |
| #20265217 | 2 |
| #20265174 | 2 |
| C2×#102×C101 | 2 |
| #3062 | 101 |