Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23757282 | C2 | semidirect |
| 5. #23757043 | C2 | semidirect |
| 6. #23757029 | C2 | semidirect |
| 7. #519×C157 | C2 | semidirect |
| 11. C2×#14578944 | C4 | semidirect |
| 12. C2×#14578941 | C4 | semidirect |
| 109. C157 | #1905 | semidirect |
| 112. #519 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| #23757291 | 2 |
| #23757282 | 2 |
| #23757246 | 2 |
| #23757043 | 2 |
| #23757029 | 2 |
| #519×C157 | 2 |
| #1905 | 157 |