Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757613 | C2 | semidirect |
| 4. #23757612 | C2 | semidirect |
| 5. #23757607 | C2 | semidirect |
| 6. #23757602 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 8. #23757309 | C2 | semidirect |
| 9. C2×#19097695 | C2 | semidirect |
| 11. #419×C157 | C2 | semidirect |
| 126. C157 | #3097 | semidirect |
| 136. #419 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757847 | 2 |
| #23757753 | 2 |
| #23757613 | 2 |
| #23757612 | 2 |
| #23757607 | 2 |
| #23757602 | 2 |
| #23757315 | 2 |
| #23757309 | 2 |
| C2×#19097695 | 2 |
| #23757241 | 2 |
| #419×C157 | 2 |
| #3097 | 157 |