Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #23757751 | C2 | semidirect |
| 4. #23757376 | C2 | semidirect |
| 5. #23757358 | C2 | semidirect |
| 6. #23757309 | C2 | semidirect |
| 8. #23757231 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 11. C2×#14578941 | C4 | semidirect |
| 16. Q8×Dic157 | C22 | semidirect |
| 23. #19097704 | C22 | semidirect |
| 24. #19097702 | C22 | semidirect |
| 26. #19097681 | C22 | semidirect |
| 27. C8×Dic157 | C22 | semidirect |
| 31. #103×C157 | C22 | semidirect |
| 38. #14578941 | C2×C4 | semidirect |
| 39. #14578941 | C2×C4 | semidirect |
| 40. C2×#11929434 | C2×C4 | semidirect |
| 54. C2×Q8×C157 | C2×C4 | semidirect |
| 103. C157 | #2949 | semidirect |
| 111. #419 | D157 | semidirect |
| 132. #103 | C2×D157 | semidirect |
| 139. C2×Q8 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| #23757751 | 2 |
| #23757747 | 2 |
| #23757376 | 2 |
| #23757358 | 2 |
| #23757309 | 2 |
| #23757279 | 2 |
| #23757231 | 2 |
| #419×C157 | 2 |
| #2949 | 157 |