Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #23757625 | C2 | semidirect |
| 5. #23757555 | C2 | semidirect |
| 7. #23757483 | C2 | semidirect |
| 8. #23757404 | C2 | semidirect |
| 9. #23757378 | C2 | semidirect |
| 11. Q82×C157 | C2 | semidirect |
| 116. C157 | #3369 | semidirect |
| 118. Q82 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757635 | 2 |
| #23757625 | 2 |
| #23757560 | 2 |
| #23757555 | 2 |
| #23757495 | 2 |
| #23757483 | 2 |
| #23757404 | 2 |
| #23757378 | 2 |
| C4×#14578941 | 2 |
| Q82×C157 | 2 |
| #3369 | 157 |