Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20261438 | C2 | semidirect |
| 2. #20261062 | C2 | semidirect |
| 3. #20261050 | C2 | semidirect |
| 4. #20261032 | C2 | semidirect |
| 5. #20260989 | C2 | semidirect |
| 6. C4×D776 | C2 | semidirect |
| 7. #20260814 | C2 | semidirect |
| 8. #20260774 | C2 | semidirect |
| 9. #499×C97 | C2 | semidirect |
| 103. C97 | #3355 | semidirect |
| 105. #499 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261438 | 2 |
| #20261062 | 2 |
| #20261050 | 2 |
| #20261032 | 2 |
| #20260989 | 2 |
| C4×D776 | 2 |
| #20260814 | 2 |
| #20260774 | 2 |
| #499×C97 | 2 |
| #3355 | 97 |