Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 2. #23757290 | C2 | semidirect |
| 3. #23757279 | C2 | semidirect |
| 4. C2×#19097687 | C2 | semidirect |
| 5. #23757045 | C2 | semidirect |
| 6. #23757031 | C2 | semidirect |
| 7. #568×C157 | C2 | semidirect |
| 11. C2×#14578941 | C4 | semidirect |
| 12. C2×#14578939 | C4 | semidirect |
| 112. C157 | #1903 | semidirect |
| 115. #568 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| #23757290 | 2 |
| #23757279 | 2 |
| C2×#19097687 | 2 |
| #23757045 | 2 |
| #23757031 | 2 |
| #568×C157 | 2 |
| #1903 | 157 |