Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20261140 | C2 | semidirect |
| 2. #20261131 | C2 | semidirect |
| 4. #20261087 | C2 | semidirect |
| 6. #20260456 | C2 | semidirect |
| 52. C8×C97 | SD16 | semidirect |
| 70. C97 | #1714 | semidirect |
| 124. C8 | #13095499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261140 | 2 |
| #20261131 | 2 |
| #20261107 | 2 |
| #20261087 | 2 |
| #20261081 | 2 |
| #20260456 | 2 |
| #492×C97 | 2 |
| #1714 | 97 |