Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 12. #19097681 | C4 | semidirect |
| 13. C8×Dic157 | C4 | semidirect |
| 72. C157 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×Dic157 | 2 |
| #23757044 | 2 |
| #23757034 | 2 |
| #23757032 | 2 |
| #23757031 | 2 |
| #23757029 | 2 |
| #344×C157 | 2 |
| #1841 | 157 |