Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23757876 | C2 | semidirect |
| 2. #23757575 | C2 | semidirect |
| 3. #23757572 | C2 | semidirect |
| 4. #23757526 | C2 | semidirect |
| 5. #23757507 | C2 | semidirect |
| 6. #23757467 | C2 | semidirect |
| 7. #23757466 | C2 | semidirect |
| 8. #23757301 | C2 | semidirect |
| 9. #469×C157 | C2 | semidirect |
| 109. C157 | #3259 | semidirect |
| 115. #469 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757876 | 2 |
| #23757575 | 2 |
| #23757572 | 2 |
| #23757526 | 2 |
| #23757507 | 2 |
| #23757467 | 2 |
| #23757466 | 2 |
| #23757301 | 2 |
| #469×C157 | 2 |
| #3259 | 157 |