Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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. #23758135 | C2 | semidirect |
| 32. #11929434 | M16 | semidirect |
| 51. C157 | #1566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758277 | 2 |
| #23758135 | 2 |
| C4×C8×D157 | 2 |
| #1566 | 157 |