Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#19097736 | C2 | semidirect |
| 3. #23757586 | C2 | semidirect |
| 4. #23757567 | C2 | semidirect |
| 5. #23757472 | C2 | semidirect |
| 6. #23757414 | C2 | semidirect |
| 7. #23757411 | C2 | semidirect |
| 8. #23757372 | C2 | semidirect |
| 9. #23757370 | C2 | semidirect |
| 10. #23757327 | C2 | semidirect |
| 11. #480×C157 | C2 | semidirect |
| 86. Dic314 | #41 | semidirect |
| 140. C157 | #3112 | semidirect |
| 145. #480 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757818 | 2 |
| C2×#19097736 | 2 |
| #23757586 | 2 |
| #23757567 | 2 |
| #23757472 | 2 |
| #23757414 | 2 |
| #23757411 | 2 |
| #23757372 | 2 |
| #23757370 | 2 |
| #23757327 | 2 |
| #480×C157 | 2 |
| #3112 | 157 |