Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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×#15690841 | C2 | semidirect |
| 2. C22×#13095498 | C2 | semidirect |
| 4. #20260957 | C2 | semidirect |
| 5. #20260935 | C2 | semidirect |
| 6. #20260762 | C2 | semidirect |
| 7. #20260739 | C2 | semidirect |
| 8. #20260729 | C2 | semidirect |
| 9. #519×C97 | C2 | semidirect |
| 13. C2×#13095501 | C22 | semidirect |
| 16. C2×#13095498 | C22 | semidirect |
| 23. C4⋊#11715895 | C22 | semidirect |
| 24. #15690733 | C22 | semidirect |
| 26. #15690730 | C22 | semidirect |
| 29. C4×Q8×C97 | C22 | semidirect |
| 55. C2×Q8×C97 | D4 | semidirect |
| 117. C97 | #3043 | semidirect |
| 121. #519 | D97 | semidirect |
| 142. C4×Q8 | C2×D97 | semidirect |
| 156. C2×Q8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| C22×#13095498 | 2 |
| #20261304 | 2 |
| #20260957 | 2 |
| #20260935 | 2 |
| #20260762 | 2 |
| #20260739 | 2 |
| #20260729 | 2 |
| #519×C97 | 2 |
| #3043 | 97 |