Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
356 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. #23757996 | C2 | semidirect |
| 2. #23757667 | C2 | semidirect |
| 4. #23757496 | C2 | semidirect |
| 6. #23757484 | C2 | semidirect |
| 7. #23757375 | C2 | semidirect |
| 8. C4×Dic628 | C2 | semidirect |
| 9. #446×C157 | C2 | semidirect |
| 102. C157 | #3402 | semidirect |
| 110. #446 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757667 | 2 |
| #23757657 | 2 |
| #23757496 | 2 |
| #23757489 | 2 |
| #23757484 | 2 |
| #23757375 | 2 |
| C4×Dic628 | 2 |
| #446×C157 | 2 |
| #3402 | 157 |