Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757676 | C2 | semidirect |
| 3. #23757606 | C2 | semidirect |
| 4. #23757597 | C2 | semidirect |
| 5. #23757558 | C2 | semidirect |
| 6. #23757550 | C2 | semidirect |
| 7. #23757521 | C2 | semidirect |
| 8. C4×#14578941 | C2 | semidirect |
| 9. #23757351 | C2 | semidirect |
| 10. #23757316 | C2 | semidirect |
| 11. #556×C157 | C2 | semidirect |
| 85. #11929434 | #41 | semidirect |
| 122. C157 | #3353 | semidirect |
| 124. #556 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757927 | 2 |
| #23757676 | 2 |
| #23757606 | 2 |
| #23757597 | 2 |
| #23757558 | 2 |
| #23757550 | 2 |
| #23757521 | 2 |
| C4×#14578941 | 2 |
| #23757351 | 2 |
| #23757316 | 2 |
| #556×C157 | 2 |
| #3353 | 157 |