Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23757976 | C2 | semidirect |
| 2. #23757600 | C2 | semidirect |
| 3. #23757588 | C2 | semidirect |
| 4. #23757570 | C2 | semidirect |
| 5. #23757527 | C2 | semidirect |
| 6. C4×D1256 | C2 | semidirect |
| 7. #23757352 | C2 | semidirect |
| 8. #23757312 | C2 | semidirect |
| 9. #499×C157 | C2 | semidirect |
| 102. C157 | #3355 | semidirect |
| 105. #499 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757976 | 2 |
| #23757600 | 2 |
| #23757588 | 2 |
| #23757570 | 2 |
| #23757527 | 2 |
| C4×D1256 | 2 |
| #23757352 | 2 |
| #23757312 | 2 |
| #499×C157 | 2 |
| #3355 | 157 |