Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#15690817 | C2 | semidirect |
| 3. #20261299 | C2 | semidirect |
| 4. #20260986 | C2 | semidirect |
| 5. #20260983 | C2 | semidirect |
| 6. #20260969 | C2 | semidirect |
| 7. #20260966 | C2 | semidirect |
| 8. #20260775 | C2 | semidirect |
| 9. #20260731 | C2 | semidirect |
| 10. C2×#15690730 | C2 | semidirect |
| 11. #537×C97 | C2 | semidirect |
| 18. C2×#13095495 | C22 | semidirect |
| 20. C22×#11715895 | C22 | semidirect |
| 27. #15690743 | C22 | semidirect |
| 28. #15690741 | C22 | semidirect |
| 29. #15690734 | C22 | semidirect |
| 30. #15690734 | C22 | semidirect |
| 31. #15690731 | C22 | semidirect |
| 32. #15690731 | C22 | semidirect |
| 38. C22⋊Q8×C97 | C22 | semidirect |
| 41. #121×C97 | C22 | semidirect |
| 53. #13095495 | D4 | semidirect |
| 152. C97 | #3062 | semidirect |
| 155. #537 | D97 | semidirect |
| 178. C22⋊Q8 | C2×D97 | semidirect |
| 183. #121 | 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 |
| C2×#15690817 | 2 |
| #20261299 | 2 |
| #20260986 | 2 |
| #20260983 | 2 |
| #20260969 | 2 |
| #20260966 | 2 |
| #20260775 | 2 |
| #20260731 | 2 |
| C2×#15690730 | 2 |
| #537×C97 | 2 |
| #3062 | 97 |