Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690836 | C2 | semidirect |
| 2. C22×#13095496 | C2 | semidirect |
| 3. #20261304 | C2 | semidirect |
| 4. #20260950 | C2 | semidirect |
| 5. #20260930 | C2 | semidirect |
| 6. #20260762 | C2 | semidirect |
| 7. #20260739 | C2 | semidirect |
| 8. #20260729 | C2 | semidirect |
| 9. #518×C97 | C2 | semidirect |
| 13. C2×#13095499 | C22 | semidirect |
| 16. C2×#13095496 | C22 | semidirect |
| 19. #15690807 | C22 | semidirect |
| 20. #15690798 | C22 | semidirect |
| 23. C4⋊#11715895 | C22 | semidirect |
| 24. #15690733 | C22 | semidirect |
| 25. #15690730 | C22 | semidirect |
| 26. #15690730 | C22 | semidirect |
| 29. C4×D4×C97 | C22 | semidirect |
| 56. C2×D4×C97 | D4 | semidirect |
| 122. C97 | #3041 | semidirect |
| 126. #518 | D97 | semidirect |
| 147. C4×D4 | C2×D97 | semidirect |
| 169. C2×D4 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690836 | 2 |
| C22×#13095496 | 2 |
| #20261304 | 2 |
| #20260950 | 2 |
| #20260930 | 2 |
| #20260762 | 2 |
| #20260739 | 2 |
| #20260729 | 2 |
| #518×C97 | 2 |
| #3041 | 97 |