Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#19097769 | C2 | semidirect |
| 5. #23757482 | C2 | semidirect |
| 6. #23757477 | C2 | semidirect |
| 7. #23757296 | C2 | semidirect |
| 8. #23757281 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 116. Dic157 | #137 | semidirect |
| 121. C157 | #3039 | semidirect |
| 131. #419 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097802 | 2 |
| C2×#19097769 | 2 |
| #23757741 | 2 |
| #23757482 | 2 |
| #23757477 | 2 |
| #23757296 | 2 |
| #23757281 | 2 |
| #419×C157 | 2 |
| #3039 | 157 |