Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #23758002 | C2 | semidirect |
| 2. #23757668 | C2 | semidirect |
| 4. #23757492 | C2 | semidirect |
| 5. #23757483 | C2 | semidirect |
| 6. #23757478 | C2 | semidirect |
| 8. #23757404 | C2 | semidirect |
| 9. #23757373 | C2 | semidirect |
| 10. C4×#14578944 | C2 | semidirect |
| 121. C157 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758002 | 2 |
| #23757668 | 2 |
| #23757645 | 2 |
| #23757492 | 2 |
| #23757483 | 2 |
| #23757478 | 2 |
| #23757470 | 2 |
| #23757404 | 2 |
| #23757373 | 2 |
| C4×#14578944 | 2 |
| #559×C157 | 2 |
| #3400 | 157 |