Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. C2×#19097818 | C2 | semidirect |
| 2. #23758071 | C2 | semidirect |
| 3. #23757844 | C2 | semidirect |
| 4. #23757454 | C2 | semidirect |
| 5. #23757444 | C2 | semidirect |
| 6. #23757290 | C2 | semidirect |
| 7. #23757289 | C2 | semidirect |
| 8. C2×#19097689 | C2 | semidirect |
| 9. #575×C157 | C2 | semidirect |
| 21. #19097802 | C22 | semidirect |
| 23. #19097797 | C22 | semidirect |
| 27. #19097769 | C22 | semidirect |
| 28. #19097758 | C22 | semidirect |
| 32. #19097698 | C22 | semidirect |
| 33. #19097697 | C22 | semidirect |
| 34. #19097689 | C22 | semidirect |
| 38. #137×C157 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C157 | C22 | semidirect |
| 185. C157 | #3020 | semidirect |
| 189. #575 | D157 | semidirect |
| 212. #137 | C2×D157 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097818 | 2 |
| #23758071 | 2 |
| #23757844 | 2 |
| #23757454 | 2 |
| #23757444 | 2 |
| #23757290 | 2 |
| #23757289 | 2 |
| C2×#19097689 | 2 |
| #575×C157 | 2 |
| #3020 | 157 |