Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23758002 | C2 | semidirect |
| 3. #23757629 | C2 | semidirect |
| 5. #23757576 | C2 | semidirect |
| 6. #23757558 | C2 | semidirect |
| 7. #23757497 | C2 | semidirect |
| 9. C8×Dic314 | C2 | semidirect |
| 10. #23757358 | C2 | semidirect |
| 11. C4×Q16×C157 | C2 | semidirect |
| 117. C157 | #3365 | semidirect |
| 128. C4×Q16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23758002 | 2 |
| #23757629 | 2 |
| #23757620 | 2 |
| #23757576 | 2 |
| #23757558 | 2 |
| #23757497 | 2 |
| #23757473 | 2 |
| C8×Dic314 | 2 |
| #23757358 | 2 |
| C4×Q16×C157 | 2 |
| #3365 | 157 |