Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23758003 | C2 | semidirect |
| 5. #23757556 | C2 | semidirect |
| 7. #23757480 | C2 | semidirect |
| 8. #23757403 | C2 | semidirect |
| 9. #23757377 | C2 | semidirect |
| 11. #487×C157 | C2 | semidirect |
| 116. C157 | #3369 | semidirect |
| 121. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758003 | 2 |
| #23757997 | 2 |
| #23757634 | 2 |
| #23757560 | 2 |
| #23757556 | 2 |
| #23757498 | 2 |
| #23757480 | 2 |
| #23757403 | 2 |
| #23757377 | 2 |
| C4×#14578943 | 2 |
| #487×C157 | 2 |
| #3369 | 157 |