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. #23757602 | C2 | semidirect |
| 4. #23757555 | C2 | semidirect |
| 5. #23757505 | C2 | semidirect |
| 6. #23757475 | C2 | semidirect |
| 7. #23757413 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. C8×D628 | C2 | semidirect |
| 10. #103×D157 | C2 | semidirect |
| 11. #487×C157 | C2 | semidirect |
| 81. Dic314 | #41 | semidirect |
| 85. D628 | SD16 | semidirect |
| 128. C157 | #3298 | semidirect |
| 132. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757938 | 2 |
| #23757926 | 2 |
| #23757602 | 2 |
| #23757555 | 2 |
| #23757505 | 2 |
| #23757475 | 2 |
| #23757413 | 2 |
| C4×#14578943 | 2 |
| C8×D628 | 2 |
| #103×D157 | 2 |
| #487×C157 | 2 |
| #3298 | 157 |