Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23757708 | C2 | semidirect |
| 2. C2×#19097712 | C2 | semidirect |
| 3. #23757543 | C2 | semidirect |
| 4. #23757086 | C2 | semidirect |
| 5. #23757080 | C2 | semidirect |
| 6. #23757057 | C2 | semidirect |
| 7. #576×C157 | C2 | semidirect |
| 9. C2×D1256 | C22 | semidirect |
| 13. #19097711 | C22 | semidirect |
| 14. C2×#14578929 | C22 | semidirect |
| 15. #19097707 | C22 | semidirect |
| 93. C157 | #2192 | semidirect |
| 95. #576 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757708 | 2 |
| C2×#19097712 | 2 |
| #23757543 | 2 |
| #23757086 | 2 |
| #23757080 | 2 |
| #23757057 | 2 |
| #576×C157 | 2 |
| #2192 | 157 |