Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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. #23757677 | C2 | semidirect |
| 3. #23757077 | C2 | semidirect |
| 6. #23757048 | C2 | semidirect |
| 7. #358×C157 | C2 | semidirect |
| 67. C157 | #2243 | semidirect |
| 72. #358 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757677 | 2 |
| #23757658 | 2 |
| #23757077 | 2 |
| #23757075 | 2 |
| #23757073 | 2 |
| #23757048 | 2 |
| #358×C157 | 2 |
| #2243 | 157 |