Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20261288 | C2 | semidirect |
| 3. #20261091 | C2 | semidirect |
| 4. #20261088 | C2 | semidirect |
| 5. #20261084 | C2 | semidirect |
| 6. #20261080 | C2 | semidirect |
| 7. #20260732 | C2 | semidirect |
| 8. #20260731 | C2 | semidirect |
| 9. #20260729 | C2 | semidirect |
| 10. C2×C8×Dic97 | C2 | semidirect |
| 11. #416×C97 | C2 | semidirect |
| 126. C97 | #3131 | semidirect |
| 136. #416 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| #20261281 | 2 |
| #20261091 | 2 |
| #20261088 | 2 |
| #20261084 | 2 |
| #20261080 | 2 |
| #20260732 | 2 |
| #20260731 | 2 |
| #20260729 | 2 |
| C2×C8×Dic97 | 2 |
| #416×C97 | 2 |
| #3131 | 97 |