Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. #23757140 | C2 | semidirect |
| 3. #23757139 | C2 | semidirect |
| 6. C4⋊C4×Dic157 | C2 | semidirect |
| 8. #23757118 | C2 | semidirect |
| 9. #382×C157 | C2 | semidirect |
| 19. C42×D157 | C4 | semidirect |
| 105. C157 | #2283 | semidirect |
| 110. #382 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D157 | 2 |
| #23757140 | 2 |
| #23757139 | 2 |
| #23757135 | 2 |
| #23757130 | 2 |
| C4⋊C4×Dic157 | 2 |
| #23757120 | 2 |
| #23757118 | 2 |
| #382×C157 | 2 |
| #2283 | 157 |