Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 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. #23758073 | C2 | semidirect |
| 2. C2×#19097797 | C2 | semidirect |
| 3. C2×#19097797 | C2 | semidirect |
| 4. #23758039 | C2 | semidirect |
| 5. #23757542 | C2 | semidirect |
| 6. #23757535 | C2 | semidirect |
| 7. #23757321 | C2 | semidirect |
| 8. #23757255 | C2 | semidirect |
| 9. C2×#100×C157 | C2 | semidirect |
| 13. #19097804 | C22 | semidirect |
| 15. #19097799 | C22 | semidirect |
| 22. C2×#14578942 | C22 | semidirect |
| 24. C2×#14578939 | C22 | semidirect |
| 25. #19097779 | C22 | semidirect |
| 30. #19097706 | C22 | semidirect |
| 31. #19097689 | C22 | semidirect |
| 32. #19097687 | C22 | semidirect |
| 36. #100×C157 | C22 | semidirect |
| 147. C157 | #3068 | semidirect |
| 157. C2×#100 | D157 | semidirect |
| 184. #100 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758073 | 2 |
| C2×#19097797 | 2 |
| #23758039 | 2 |
| #23757542 | 2 |
| #23757535 | 2 |
| #23757321 | 2 |
| #23757255 | 2 |
| C2×#100×C157 | 2 |
| #3068 | 157 |