Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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 |
|---|---|---|
| 1. C2×#19097790 | C2 | semidirect |
| 2. C22×Dic628 | C2 | semidirect |
| 3. #23757929 | C2 | semidirect |
| 4. #23757656 | C2 | semidirect |
| 5. #23757515 | C2 | semidirect |
| 6. #23757494 | C2 | semidirect |
| 7. #23757436 | C2 | semidirect |
| 8. #23757411 | C2 | semidirect |
| 9. #23757367 | C2 | semidirect |
| 10. C8×C22⋊D157 | C2 | semidirect |
| 11. #466×C157 | C2 | semidirect |
| 55. Dic628 | D4 | semidirect |
| 116. C22×C157 | #135 | semidirect |
| 136. C157 | #3285 | semidirect |
| 143. #466 | D157 | semidirect |
| 256. C22 | #19097790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097790 | 2 |
| C22×Dic628 | 2 |
| #23757929 | 2 |
| #23757656 | 2 |
| #23757515 | 2 |
| #23757494 | 2 |
| #23757436 | 2 |
| #23757411 | 2 |
| #23757367 | 2 |
| C8×C22⋊D157 | 2 |
| #466×C157 | 2 |
| #3285 | 157 |