Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757938 | C2 | semidirect |
| 3. #23757623 | C2 | semidirect |
| 4. #23757602 | C2 | semidirect |
| 5. #23757559 | C2 | semidirect |
| 6. #23757499 | C2 | semidirect |
| 7. #23757410 | C2 | semidirect |
| 8. C4×#14578942 | C2 | semidirect |
| 9. #23757338 | C2 | semidirect |
| 10. #103×D157 | C2 | semidirect |
| 11. #461×C157 | C2 | semidirect |
| 81. Dic314 | #41 | semidirect |
| 82. D628 | SD16 | semidirect |
| 128. C157 | #3298 | semidirect |
| 136. #461 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757938 | 2 |
| #23757928 | 2 |
| #23757623 | 2 |
| #23757602 | 2 |
| #23757559 | 2 |
| #23757499 | 2 |
| #23757410 | 2 |
| C4×#14578942 | 2 |
| #23757338 | 2 |
| #103×D157 | 2 |
| #461×C157 | 2 |
| #3298 | 157 |