Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #23758164 | C2 | semidirect |
| 4. #23758163 | C2 | semidirect |
| 9. #19097845 | C4 | semidirect |
| 10. D157⋊C16 | C4 | semidirect |
| 16. #19097711 | C4 | semidirect |
| 18. C16×D157 | C4 | semidirect |
| 19. M32×C157 | C4 | semidirect |
| 28. #14578957 | C2×C4 | semidirect |
| 35. #14578929 | C2×C4 | semidirect |
| 37. C16×C157 | C2×C4 | semidirect |
| 67. D157 | #347 | semidirect |
| 68. C157 | C2×#347 | semidirect |
| 82. M32 | #10597845 | semidirect |
| 106. C16 | C2×#10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D157⋊M32 | 2 |
| C2×#19097825 | 2 |
| #23758164 | 2 |
| #23758163 | 2 |
| M32×D157 | 2 |
| C2×#347 | 157 |