Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757989 | C2 | semidirect |
| 2. #23757945 | C2 | semidirect |
| 3. #23757621 | C2 | semidirect |
| 4. #23757600 | C2 | semidirect |
| 5. #23757510 | C2 | semidirect |
| 6. #23757469 | C2 | semidirect |
| 7. #23757421 | C2 | semidirect |
| 8. C4×#14578941 | C2 | semidirect |
| 9. #23757338 | C2 | semidirect |
| 10. #23757268 | C2 | semidirect |
| 11. #477×C157 | C2 | semidirect |
| 132. C157 | #3305 | semidirect |
| 138. #477 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757989 | 2 |
| #23757945 | 2 |
| #23757621 | 2 |
| #23757600 | 2 |
| #23757510 | 2 |
| #23757469 | 2 |
| #23757421 | 2 |
| C4×#14578941 | 2 |
| #23757338 | 2 |
| #23757268 | 2 |
| #477×C157 | 2 |
| #3305 | 157 |