Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097793 | C2 | semidirect |
| 3. C2×#19097777 | C2 | semidirect |
| 4. #23757549 | C2 | semidirect |
| 5. #23757544 | C2 | semidirect |
| 6. #23757537 | C2 | semidirect |
| 7. #23757255 | C2 | semidirect |
| 8. C2×#108×C157 | C2 | semidirect |
| 20. C2×Dic628 | C22 | semidirect |
| 21. C2×#14578943 | C22 | semidirect |
| 22. C2×D1256 | C22 | semidirect |
| 30. #19097689 | C22 | semidirect |
| 31. #19097687 | C22 | semidirect |
| 34. #108×C157 | C22 | semidirect |
| 35. #108×C157 | C22 | semidirect |
| 132. C157 | #3067 | semidirect |
| 140. C2×#108 | D157 | semidirect |
| 165. #108 | C2×D157 | semidirect |
| 166. #108 | 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×#19097793 | 2 |
| C2×#19097777 | 2 |
| #23757549 | 2 |
| #23757544 | 2 |
| #23757537 | 2 |
| #23757255 | 2 |
| C2×#108×C157 | 2 |
| #3067 | 157 |