Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20261270 | C2 | semidirect |
| 2. #20261119 | C2 | semidirect |
| 3. #20261092 | C2 | semidirect |
| 4. #20260977 | C2 | semidirect |
| 6. #20260965 | C2 | semidirect |
| 7. #20260829 | C2 | semidirect |
| 8. #20260822 | C2 | semidirect |
| 9. #20260817 | C2 | semidirect |
| 10. C4×C8×D97 | C2 | semidirect |
| 11. #499×C97 | C2 | semidirect |
| 119. C97 | #3168 | semidirect |
| 121. #499 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261270 | 2 |
| #20261119 | 2 |
| #20261092 | 2 |
| #20260977 | 2 |
| #20260972 | 2 |
| #20260965 | 2 |
| #20260829 | 2 |
| #20260822 | 2 |
| #20260817 | 2 |
| C4×C8×D97 | 2 |
| #499×C97 | 2 |
| #3168 | 97 |