Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #20261363 | C2 | semidirect |
| 2. #20261099 | C2 | semidirect |
| 3. #20261094 | C2 | semidirect |
| 4. #20261089 | C2 | semidirect |
| 5. #20261081 | C2 | semidirect |
| 6. #20260740 | C2 | semidirect |
| 7. #20260736 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 9. C2×#15690731 | C2 | semidirect |
| 10. #20260691 | C2 | semidirect |
| 14. #15690810 | C22 | semidirect |
| 16. #15690802 | C22 | semidirect |
| 21. #15690734 | C22 | semidirect |
| 22. #15690734 | C22 | semidirect |
| 23. #15690734 | C22 | semidirect |
| 28. #15690731 | C22 | semidirect |
| 29. #15690731 | C22 | semidirect |
| 30. #15690731 | C22 | semidirect |
| 31. #15690721 | C22 | semidirect |
| 32. C4×#11715895 | C22 | semidirect |
| 136. C97 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261099 | 2 |
| #20261094 | 2 |
| #20261089 | 2 |
| #20261081 | 2 |
| #20260740 | 2 |
| #20260736 | 2 |
| #20260731 | 2 |
| C2×#15690731 | 2 |
| #20260691 | 2 |
| #535×C97 | 2 |
| #3136 | 97 |