Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #23757989 | C2 | semidirect |
| 2. #23757926 | C2 | semidirect |
| 3. #23757613 | C2 | semidirect |
| 4. #23757560 | C2 | semidirect |
| 5. #23757505 | C2 | semidirect |
| 6. #23757475 | C2 | semidirect |
| 7. #23757421 | C2 | semidirect |
| 8. C4×D1256 | C2 | semidirect |
| 9. C8×D628 | C2 | semidirect |
| 10. #23757268 | C2 | semidirect |
| 11. #487×C157 | C2 | semidirect |
| 130. C157 | #3303 | semidirect |
| 134. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757989 | 2 |
| #23757926 | 2 |
| #23757613 | 2 |
| #23757560 | 2 |
| #23757505 | 2 |
| #23757475 | 2 |
| #23757421 | 2 |
| C4×D1256 | 2 |
| C8×D628 | 2 |
| #23757268 | 2 |
| #487×C157 | 2 |
| #3303 | 157 |