Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #23757998 | C2 | semidirect |
| 3. #23757664 | C2 | semidirect |
| 4. #23757493 | C2 | semidirect |
| 5. #23757480 | C2 | semidirect |
| 6. #23757476 | C2 | semidirect |
| 8. #23757403 | C2 | semidirect |
| 9. #23757374 | C2 | semidirect |
| 10. C4×Dic628 | 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 |
|---|---|
| #23758009 | 2 |
| #23757998 | 2 |
| #23757664 | 2 |
| #23757493 | 2 |
| #23757480 | 2 |
| #23757476 | 2 |
| #23757470 | 2 |
| #23757403 | 2 |
| #23757374 | 2 |
| C4×Dic628 | 2 |
| #492×C157 | 2 |
| #3400 | 157 |