Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23758078 | C2 | semidirect |
| 2. #23757714 | C2 | semidirect |
| 3. #23757708 | C2 | semidirect |
| 4. #23757703 | C2 | semidirect |
| 5. C2×#19097714 | C2 | semidirect |
| 6. #23757690 | C2 | semidirect |
| 7. #578×C157 | C2 | semidirect |
| 12. #19097717 | C22 | semidirect |
| 13. #19097715 | C22 | semidirect |
| 14. #19097714 | C22 | semidirect |
| 15. #19097714 | C22 | semidirect |
| 16. #19097712 | C22 | semidirect |
| 17. #19097711 | C22 | semidirect |
| 18. C2×#14578929 | C22 | semidirect |
| 21. #135×C157 | C22 | semidirect |
| 22. C2×Q16×C157 | C22 | semidirect |
| 74. C157 | #3416 | semidirect |
| 76. #578 | D157 | semidirect |
| 88. #135 | C2×D157 | semidirect |
| 89. C2×Q16 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758078 | 2 |
| #23757714 | 2 |
| #23757708 | 2 |
| #23757703 | 2 |
| C2×#19097714 | 2 |
| #23757690 | 2 |
| #578×C157 | 2 |
| #3416 | 157 |