Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757997 | C2 | semidirect |
| 3. #23757610 | C2 | semidirect |
| 4. #23757600 | C2 | semidirect |
| 5. #23757555 | C2 | semidirect |
| 6. #23757550 | C2 | semidirect |
| 7. #23757520 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. #23757352 | C2 | semidirect |
| 10. #23757314 | C2 | semidirect |
| 11. #500×C157 | C2 | semidirect |
| 99. C8×C157 | #41 | semidirect |
| 122. C157 | #3353 | semidirect |
| 126. #500 | D157 | semidirect |
| 222. C8 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757926 | 2 |
| #23757610 | 2 |
| #23757600 | 2 |
| #23757555 | 2 |
| #23757550 | 2 |
| #23757520 | 2 |
| C4×#14578943 | 2 |
| #23757352 | 2 |
| #23757314 | 2 |
| #500×C157 | 2 |
| #3353 | 157 |