Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 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. #23757997 | C2 | semidirect |
| 2. #23757984 | C2 | semidirect |
| 3. #23757629 | C2 | semidirect |
| 4. #23757582 | C2 | semidirect |
| 5. #23757560 | C2 | semidirect |
| 7. #23757475 | C2 | semidirect |
| 8. C8×Dic314 | C2 | semidirect |
| 9. #23757358 | C2 | semidirect |
| 11. #487×C157 | C2 | semidirect |
| 120. C157 | #3360 | semidirect |
| 125. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757984 | 2 |
| #23757629 | 2 |
| #23757582 | 2 |
| #23757560 | 2 |
| #23757491 | 2 |
| #23757475 | 2 |
| C8×Dic314 | 2 |
| #23757358 | 2 |
| C4×D1256 | 2 |
| #487×C157 | 2 |
| #3360 | 157 |