Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23757847 | C2 | semidirect |
| 3. #23757756 | C2 | semidirect |
| 4. #23757497 | C2 | semidirect |
| 5. #23757490 | C2 | semidirect |
| 6. #23757481 | C2 | semidirect |
| 7. #23757476 | C2 | semidirect |
| 8. #23757301 | C2 | semidirect |
| 9. #23757275 | C2 | semidirect |
| 10. C2×#19097695 | C2 | semidirect |
| 11. C2×#137×C157 | C2 | semidirect |
| 146. C157 | #3046 | semidirect |
| 148. C2×#137 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| #23757847 | 2 |
| #23757756 | 2 |
| #23757497 | 2 |
| #23757490 | 2 |
| #23757481 | 2 |
| #23757476 | 2 |
| #23757301 | 2 |
| #23757275 | 2 |
| C2×#19097695 | 2 |
| C2×#137×C157 | 2 |
| #3046 | 157 |