Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #23757371 | C2 | semidirect |
| 4. C4×#14578941 | C2 | semidirect |
| 5. #23757309 | C2 | semidirect |
| 6. #23757282 | C2 | semidirect |
| 8. #23757229 | C2 | semidirect |
| 9. #519×C157 | C2 | semidirect |
| 11. C2×#14578941 | C4 | semidirect |
| 20. #19097704 | C22 | semidirect |
| 21. #19097702 | C22 | semidirect |
| 22. #19097695 | C22 | semidirect |
| 24. #19097682 | C22 | semidirect |
| 25. C4×#11929434 | C22 | semidirect |
| 28. C4×Q8×C157 | C22 | semidirect |
| 38. #14578941 | C2×C4 | semidirect |
| 39. #14578941 | C2×C4 | semidirect |
| 41. C2×#11929434 | C2×C4 | semidirect |
| 51. C2×Q8×C157 | C2×C4 | semidirect |
| 103. C157 | #2949 | semidirect |
| 106. #519 | D157 | semidirect |
| 122. C4×Q8 | 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 |
| #23757747 | 2 |
| #23757371 | 2 |
| C4×#14578941 | 2 |
| #23757309 | 2 |
| #23757282 | 2 |
| #23757277 | 2 |
| #23757229 | 2 |
| #519×C157 | 2 |
| #2949 | 157 |