Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #23757998 | C2 | semidirect |
| 3. #23757629 | C2 | semidirect |
| 5. #23757572 | C2 | semidirect |
| 6. #23757498 | C2 | semidirect |
| 8. #23757397 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 10. #23757360 | C2 | semidirect |
| 11. #475×C157 | C2 | semidirect |
| 117. C157 | #3365 | semidirect |
| 124. #475 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23757998 | 2 |
| #23757629 | 2 |
| #23757621 | 2 |
| #23757572 | 2 |
| #23757498 | 2 |
| #23757474 | 2 |
| #23757397 | 2 |
| C4×#14578944 | 2 |
| #23757360 | 2 |
| #475×C157 | 2 |
| #3365 | 157 |