Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 141 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. C157⋊#401 | C2 | semidirect |
| 2. #23757214 | C2 | semidirect |
| 5. C4×#14578933 | C2 | semidirect |
| 7. #376×C157 | C2 | semidirect |
| 70. C157 | #2401 | semidirect |
| 78. #376 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C157⋊#401 | 2 |
| #23757214 | 2 |
| #23757202 | 2 |
| #23757197 | 2 |
| C4×#14578933 | 2 |
| C4×#14578931 | 2 |
| #376×C157 | 2 |
| #2401 | 157 |