Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #23757630 | C2 | semidirect |
| 4. #23757570 | C2 | semidirect |
| 5. #23757555 | C2 | semidirect |
| 6. #23757495 | C2 | semidirect |
| 8. Q8×#11929434 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 10. C4×#14578941 | C2 | semidirect |
| 11. #557×C157 | C2 | semidirect |
| 117. C157 | #3365 | semidirect |
| 120. #557 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23757630 | 2 |
| #23757621 | 2 |
| #23757570 | 2 |
| #23757555 | 2 |
| #23757495 | 2 |
| #23757473 | 2 |
| Q8×#11929434 | 2 |
| C4×#14578944 | 2 |
| C4×#14578941 | 2 |
| #557×C157 | 2 |
| #3365 | 157 |