Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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. #23757826 | C2 | semidirect |
| 3. #23757634 | C2 | semidirect |
| 4. #23757629 | C2 | semidirect |
| 5. #23757282 | C2 | semidirect |
| 8. M16×Dic157 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 12. #19097770 | C22 | semidirect |
| 13. #19097762 | C22 | semidirect |
| 22. #19097695 | C22 | semidirect |
| 25. #19097681 | C22 | semidirect |
| 26. C8×Dic157 | C22 | semidirect |
| 30. #103×C157 | C22 | semidirect |
| 104. C157 | #3140 | semidirect |
| 111. #419 | D157 | semidirect |
| 131. #103 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757826 | 2 |
| C2×#19097760 | 2 |
| #23757634 | 2 |
| #23757629 | 2 |
| #23757282 | 2 |
| #23757279 | 2 |
| #23757277 | 2 |
| M16×Dic157 | 2 |
| #419×C157 | 2 |
| #3140 | 157 |