Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23757050 | C2 | semidirect |
| 7. #19097711 | C4 | semidirect |
| 9. C2×#14578929 | C4 | semidirect |
| 13. M32×C157 | C4 | semidirect |
| 15. C2×C16×C157 | C4 | semidirect |
| 57. C157 | #2110 | semidirect |
| 68. M32 | Dic157 | semidirect |
| 71. C2×C16 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097711 | 2 |
| #23757228 | 2 |
| #23757050 | 2 |
| C2×M32×C157 | 2 |
| #2110 | 157 |