Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19097804 | C2 | semidirect |
| 3. C22×#14578944 | C2 | semidirect |
| 4. #23757849 | C2 | semidirect |
| 5. #23757438 | C2 | semidirect |
| 6. #23757430 | C2 | semidirect |
| 7. #23757267 | C2 | semidirect |
| 8. #23757241 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 140. C157 | #3011 | semidirect |
| 148. #419 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097819 | 2 |
| C2×#19097804 | 2 |
| C22×#14578944 | 2 |
| #23757849 | 2 |
| #23757438 | 2 |
| #23757430 | 2 |
| #23757267 | 2 |
| #23757241 | 2 |
| #419×C157 | 2 |
| #3011 | 157 |