Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #20261460 | C2 | semidirect |
| 3. #20261126 | C2 | semidirect |
| 4. #20260955 | C2 | semidirect |
| 5. #20260942 | C2 | semidirect |
| 6. #20260938 | C2 | semidirect |
| 8. #20260865 | C2 | semidirect |
| 9. #20260836 | C2 | semidirect |
| 10. C4×Dic388 | C2 | semidirect |
| 122. C97 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261471 | 2 |
| #20261460 | 2 |
| #20261126 | 2 |
| #20260955 | 2 |
| #20260942 | 2 |
| #20260938 | 2 |
| #20260932 | 2 |
| #20260865 | 2 |
| #20260836 | 2 |
| C4×Dic388 | 2 |
| #492×C97 | 2 |
| #3400 | 97 |