Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 1. #23758002 | C2 | semidirect |
| 4. #23757623 | C2 | semidirect |
| 5. #23757582 | C2 | semidirect |
| 8. #23757397 | C2 | semidirect |
| 9. Q16×Dic157 | C2 | semidirect |
| 11. #462×C157 | C2 | semidirect |
| 115. C157 | #3364 | semidirect |
| 124. #462 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758002 | 2 |
| #23757997 | 2 |
| #23757629 | 2 |
| #23757623 | 2 |
| #23757582 | 2 |
| #23757554 | 2 |
| #23757497 | 2 |
| #23757397 | 2 |
| Q16×Dic157 | 2 |
| C4×#14578941 | 2 |
| #462×C157 | 2 |
| #3364 | 157 |