Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#19097804 | C2 | semidirect |
| 3. #23757844 | C2 | semidirect |
| 4. #23757458 | C2 | semidirect |
| 5. #23757453 | C2 | semidirect |
| 6. #23757289 | C2 | semidirect |
| 7. #413×C157 | C2 | semidirect |
| 16. C22×Dic314 | C22 | semidirect |
| 18. #19097804 | C22 | semidirect |
| 21. #19097769 | C22 | semidirect |
| 22. #19097758 | C22 | semidirect |
| 25. #19097730 | C22 | semidirect |
| 26. #19097697 | C22 | semidirect |
| 28. C2×M16×C157 | C22 | semidirect |
| 29. #101×C157 | C22 | semidirect |
| 30. #100×C157 | C22 | semidirect |
| 129. C157 | #3022 | semidirect |
| 137. #413 | D157 | semidirect |
| 152. C2×M16 | C2×D157 | semidirect |
| 159. #101 | C2×D157 | semidirect |
| 160. #100 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758109 | 2 |
| C2×#19097804 | 2 |
| #23757844 | 2 |
| #23757458 | 2 |
| #23757453 | 2 |
| #23757289 | 2 |
| #413×C157 | 2 |
| #3022 | 157 |