Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757901 | C2 | semidirect |
| 3. #23757583 | C2 | semidirect |
| 4. #23757572 | C2 | semidirect |
| 5. #23757567 | C2 | semidirect |
| 6. #23757552 | C2 | semidirect |
| 7. C2×#19097704 | C2 | semidirect |
| 8. #23757301 | C2 | semidirect |
| 11. #428×C157 | C2 | semidirect |
| 42. #14578954 | Q8 | semidirect |
| 123. C157 | #3083 | semidirect |
| 131. #428 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757901 | 2 |
| #23757754 | 2 |
| #23757583 | 2 |
| #23757572 | 2 |
| #23757567 | 2 |
| #23757552 | 2 |
| C2×#19097704 | 2 |
| #23757301 | 2 |
| #23757275 | 2 |
| #23757267 | 2 |
| #428×C157 | 2 |
| #3083 | 157 |