Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757904 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757634 | C2 | semidirect |
| 5. #23757629 | C2 | semidirect |
| 6. #23757618 | C2 | semidirect |
| 7. #23757279 | C2 | semidirect |
| 8. #23757269 | C2 | semidirect |
| 9. C2×#19097691 | C2 | semidirect |
| 10. #23757231 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 15. #19097770 | C22 | semidirect |
| 18. #19097762 | C22 | semidirect |
| 26. #19097695 | C22 | semidirect |
| 27. #19097695 | C22 | semidirect |
| 30. #19097692 | C22 | semidirect |
| 31. #19097692 | C22 | semidirect |
| 34. #19097681 | C22 | semidirect |
| 35. C8×Dic157 | C22 | semidirect |
| 39. #103×C157 | C22 | semidirect |
| 40. #102×C157 | C22 | semidirect |
| 135. C157 | #3136 | semidirect |
| 144. #417 | D157 | semidirect |
| 167. #103 | C2×D157 | semidirect |
| 174. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757904 | 2 |
| #23757837 | 2 |
| #23757636 | 2 |
| #23757634 | 2 |
| #23757629 | 2 |
| #23757618 | 2 |
| #23757279 | 2 |
| #23757269 | 2 |
| C2×#19097691 | 2 |
| #23757231 | 2 |
| #417×C157 | 2 |
| #3136 | 157 |