Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 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. #20261571 | C2 | semidirect |
| 2. #20261552 | C2 | semidirect |
| 3. #20261547 | C2 | semidirect |
| 4. #20261540 | C2 | semidirect |
| 5. #20261535 | C2 | semidirect |
| 6. C2×#15690832 | C2 | semidirect |
| 7. C2×#131×C97 | C2 | semidirect |
| 9. #15690857 | C22 | semidirect |
| 10. #15690856 | C22 | semidirect |
| 12. C2×#13095511 | C22 | semidirect |
| 14. #15690843 | C22 | semidirect |
| 15. #15690838 | C22 | semidirect |
| 16. #15690832 | C22 | semidirect |
| 17. #15690832 | C22 | semidirect |
| 18. #15690832 | C22 | semidirect |
| 19. #15690832 | C22 | semidirect |
| 20. C2×Dic388 | C22 | semidirect |
| 21. C2×#13095500 | C22 | semidirect |
| 22. C2×D776 | C22 | semidirect |
| 24. #131×C97 | C22 | semidirect |
| 25. #131×C97 | C22 | semidirect |
| 26. C2×M16×C97 | C22 | semidirect |
| 27. C22×C8×C97 | C22 | semidirect |
| 90. C97 | #3584 | semidirect |
| 97. C2×#131 | D97 | semidirect |
| 114. #131 | C2×D97 | semidirect |
| 115. #131 | C2×D97 | semidirect |
| 116. C2×M16 | C2×D97 | semidirect |
| 117. C22×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261571 | 2 |
| #20261552 | 2 |
| #20261547 | 2 |
| #20261540 | 2 |
| #20261535 | 2 |
| C2×#15690832 | 2 |
| C2×#131×C97 | 2 |
| #3584 | 97 |