Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690835 | C2 | semidirect |
| 2. C22×#13095496 | C2 | semidirect |
| 3. #20261209 | C2 | semidirect |
| 4. #20260947 | C2 | semidirect |
| 5. #20260927 | C2 | semidirect |
| 6. #20260762 | C2 | semidirect |
| 7. #20260740 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 9. #535×C97 | C2 | semidirect |
| 12. C2×#13095498 | C22 | semidirect |
| 15. C2×#13095496 | C22 | semidirect |
| 18. C4×D388 | C22 | semidirect |
| 22. C4⋊#11715895 | C22 | semidirect |
| 23. #15690734 | C22 | semidirect |
| 24. #15690731 | C22 | semidirect |
| 25. #15690731 | C22 | semidirect |
| 28. #127×C97 | C22 | semidirect |
| 29. #124×C97 | C22 | semidirect |
| 36. C2×D388 | D4 | semidirect |
| 122. C97 | #3041 | semidirect |
| 125. #535 | D97 | semidirect |
| 142. #127 | C2×D97 | semidirect |
| 143. #124 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C22×#13095496 | 2 |
| #20261209 | 2 |
| #20260947 | 2 |
| #20260927 | 2 |
| #20260762 | 2 |
| #20260740 | 2 |
| #20260731 | 2 |
| #535×C97 | 2 |
| #3041 | 97 |