Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 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 |
|---|---|---|
| 1. #23757689 | C2 | semidirect |
| 3. #23757093 | C2 | semidirect |
| 4. #23757058 | C2 | semidirect |
| 5. #23757057 | C2 | semidirect |
| 6. #23757048 | C2 | semidirect |
| 7. #504×C157 | C2 | semidirect |
| 71. C157 | #2171 | semidirect |
| 74. #504 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757689 | 2 |
| #23757388 | 2 |
| #23757093 | 2 |
| #23757058 | 2 |
| #23757057 | 2 |
| #23757048 | 2 |
| #504×C157 | 2 |
| #2171 | 157 |