Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23757300 | C2 | semidirect |
| 4. C2×#19097690 | C2 | semidirect |
| 6. #23757037 | C2 | semidirect |
| 7. #419×C157 | C2 | semidirect |
| 100. C157 | #2046 | semidirect |
| 104. #419 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| #23757300 | 2 |
| #23757277 | 2 |
| C2×#19097690 | 2 |
| C2×#19097687 | 2 |
| #23757037 | 2 |
| #419×C157 | 2 |
| #2046 | 157 |