Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23757652 | C2 | semidirect |
| 3. #23757621 | C2 | semidirect |
| 4. #23757620 | C2 | semidirect |
| 5. #23757619 | C2 | semidirect |
| 6. C8×#11929434 | C2 | semidirect |
| 7. #486×C157 | C2 | semidirect |
| 74. C157 | #1709 | semidirect |
| 81. #486 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757652 | 2 |
| #23757649 | 2 |
| #23757621 | 2 |
| #23757620 | 2 |
| #23757619 | 2 |
| C8×#11929434 | 2 |
| #486×C157 | 2 |
| #1709 | 157 |