Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
314 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 197 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. #23757404 | C2 | semidirect |
| 50. C157 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757404 | 2 |
| #23757334 | 2 |
| #23757330 | 2 |
| #533×C157 | 2 |
| #2987 | 157 |