Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23757821 | C2 | semidirect |
| 2. #23757808 | C2 | semidirect |
| 3. #23757683 | C2 | semidirect |
| 4. #23757660 | C2 | semidirect |
| 5. #23757633 | C2 | semidirect |
| 6. #23757525 | C2 | semidirect |
| 7. #23757518 | C2 | semidirect |
| 8. #23757364 | C2 | semidirect |
| 9. #23757353 | C2 | semidirect |
| 10. #23757225 | C2 | semidirect |
| 11. #490×C157 | C2 | semidirect |
| 99. #11929434 | #41 | semidirect |
| 137. C157 | #3171 | semidirect |
| 143. #490 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757821 | 2 |
| #23757808 | 2 |
| #23757683 | 2 |
| #23757660 | 2 |
| #23757633 | 2 |
| #23757525 | 2 |
| #23757518 | 2 |
| #23757364 | 2 |
| #23757353 | 2 |
| #23757225 | 2 |
| #490×C157 | 2 |
| #3171 | 157 |