Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23757821 | C2 | semidirect |
| 2. C4×#14578953 | C2 | semidirect |
| 3. #23757596 | C2 | semidirect |
| 4. #23757559 | C2 | semidirect |
| 5. #23757553 | C2 | semidirect |
| 6. #23757470 | C2 | semidirect |
| 7. #23757415 | C2 | semidirect |
| 8. #23757385 | C2 | semidirect |
| 9. #23757370 | C2 | semidirect |
| 10. #23757329 | C2 | semidirect |
| 11. #459×C157 | C2 | semidirect |
| 86. Dic314 | #41 | semidirect |
| 110. D4×C157 | #41 | semidirect |
| 144. C157 | #3115 | semidirect |
| 152. #459 | D157 | semidirect |
| 241. D4 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757821 | 2 |
| C4×#14578953 | 2 |
| #23757596 | 2 |
| #23757559 | 2 |
| #23757553 | 2 |
| #23757470 | 2 |
| #23757415 | 2 |
| #23757385 | 2 |
| #23757370 | 2 |
| #23757329 | 2 |
| #459×C157 | 2 |
| #3115 | 157 |