Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23758001 | C2 | semidirect |
| 4. #23757653 | C2 | semidirect |
| 6. #23757483 | C2 | semidirect |
| 7. #23757482 | C2 | semidirect |
| 9. #23757403 | C2 | semidirect |
| 10. #23757379 | C2 | semidirect |
| 119. C157 | #3398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758001 | 2 |
| #23757993 | 2 |
| #23757664 | 2 |
| #23757653 | 2 |
| #23757494 | 2 |
| #23757483 | 2 |
| #23757482 | 2 |
| #23757478 | 2 |
| #23757403 | 2 |
| #23757379 | 2 |
| C4×SD16×C157 | 2 |
| #3398 | 157 |