Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23757316 | C2 | semidirect |
| 5. #23757139 | C2 | semidirect |
| 6. #23757041 | C2 | semidirect |
| 7. #339×C157 | C2 | semidirect |
| 19. #19097699 | C4 | semidirect |
| 38. #14578938 | C2×C4 | semidirect |
| 57. C42×C157 | C2×C4 | semidirect |
| 111. C157 | #1860 | semidirect |
| 119. #339 | D157 | semidirect |
| 169. C42 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757753 | 2 |
| #23757316 | 2 |
| C2×#19097699 | 2 |
| #23757275 | 2 |
| #23757139 | 2 |
| #23757041 | 2 |
| #339×C157 | 2 |
| #1860 | 157 |