Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 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. #23757997 | C2 | semidirect |
| 2. #23757943 | C2 | semidirect |
| 3. #23757659 | C2 | semidirect |
| 4. #23757490 | C2 | semidirect |
| 5. #23757475 | C2 | semidirect |
| 6. #23757471 | C2 | semidirect |
| 7. #23757465 | C2 | semidirect |
| 8. #23757403 | C2 | semidirect |
| 9. #23757374 | C2 | semidirect |
| 10. C4×D1256 | C2 | semidirect |
| 11. #492×C157 | C2 | semidirect |
| 106. C8×C157 | #41 | semidirect |
| 132. C157 | #3397 | semidirect |
| 137. #492 | D157 | semidirect |
| 239. C8 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757943 | 2 |
| #23757659 | 2 |
| #23757490 | 2 |
| #23757475 | 2 |
| #23757471 | 2 |
| #23757465 | 2 |
| #23757403 | 2 |
| #23757374 | 2 |
| C4×D1256 | 2 |
| #492×C157 | 2 |
| #3397 | 157 |