Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 1. #23757823 | C2 | semidirect |
| 2. C4×#14578954 | C2 | semidirect |
| 3. #23757598 | C2 | semidirect |
| 4. #23757559 | C2 | semidirect |
| 5. #23757554 | C2 | semidirect |
| 6. #23757474 | C2 | semidirect |
| 7. #23757469 | C2 | semidirect |
| 8. #23757420 | C2 | semidirect |
| 9. #23757386 | C2 | semidirect |
| 10. #23757375 | C2 | semidirect |
| 11. #432×C157 | C2 | semidirect |
| 87. Dic314 | #41 | semidirect |
| 93. D628 | #41 | semidirect |
| 144. C157 | #3115 | semidirect |
| 156. #432 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| C4×#14578954 | 2 |
| #23757598 | 2 |
| #23757559 | 2 |
| #23757554 | 2 |
| #23757474 | 2 |
| #23757469 | 2 |
| #23757420 | 2 |
| #23757386 | 2 |
| #23757375 | 2 |
| #432×C157 | 2 |
| #3115 | 157 |