Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #23757625 | C2 | semidirect |
| 4. #23757577 | C2 | semidirect |
| 7. #23757483 | C2 | semidirect |
| 8. Q8×#11929434 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 11. #557×C157 | C2 | semidirect |
| 115. C157 | #3364 | semidirect |
| 117. #557 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757630 | 2 |
| #23757625 | 2 |
| #23757577 | 2 |
| #23757550 | 2 |
| #23757495 | 2 |
| #23757483 | 2 |
| Q8×#11929434 | 2 |
| C4×#14578944 | 2 |
| C4×#14578941 | 2 |
| #557×C157 | 2 |
| #3364 | 157 |