Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23758090 | C2 | semidirect |
| 2. #23758083 | C2 | semidirect |
| 3. #23758074 | C2 | semidirect |
| 4. #23757656 | C2 | semidirect |
| 5. #23757549 | C2 | semidirect |
| 6. #23757535 | C2 | semidirect |
| 7. #23757453 | C2 | semidirect |
| 8. #23757444 | C2 | semidirect |
| 9. #23757389 | C2 | semidirect |
| 10. #23757388 | C2 | semidirect |
| 11. #472×C157 | C2 | semidirect |
| 12. #19097818 | C22 | semidirect |
| 16. #19097804 | C22 | semidirect |
| 27. C2×Dic628 | C22 | semidirect |
| 28. C2×#14578942 | C22 | semidirect |
| 31. #19097779 | C22 | semidirect |
| 33. #19097758 | C22 | semidirect |
| 34. #19097706 | C22 | semidirect |
| 35. #19097698 | C22 | semidirect |
| 37. #19097697 | C22 | semidirect |
| 38. #19097689 | C22 | semidirect |
| 39. C8×Dic157 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C157 | C22 | semidirect |
| 42. #131×C157 | C22 | semidirect |
| 43. #108×C157 | C22 | semidirect |
| 44. #100×C157 | C22 | semidirect |
| 149. C157 | #3290 | semidirect |
| 156. #472 | D157 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D157 | semidirect |
| 185. #131 | C2×D157 | semidirect |
| 188. #108 | C2×D157 | semidirect |
| 193. #100 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758090 | 2 |
| #23758083 | 2 |
| #23758074 | 2 |
| #23757656 | 2 |
| #23757549 | 2 |
| #23757535 | 2 |
| #23757453 | 2 |
| #23757444 | 2 |
| #23757389 | 2 |
| #23757388 | 2 |
| #472×C157 | 2 |
| #3290 | 157 |