Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14578941 | C2 | semidirect |
| 2. C22×#14578937 | C2 | semidirect |
| 3. C2×#19097747 | C2 | semidirect |
| 5. #23757522 | C2 | direct (N × H) |
| 6. C2×#19097704 | C2 | semidirect |
| 7. C2×#19097693 | C2 | semidirect |
| 8. C2×#103×C157 | C2 | semidirect |
| 13. C2×#14578941 | C22 | semidirect |
| 15. C2×#14578937 | C22 | semidirect |
| 18. #19097747 | C22 | semidirect |
| 25. #19097704 | C22 | semidirect |
| 26. #19097693 | C22 | semidirect |
| 30. #103×C157 | C22 | semidirect |
| 47. C2×#11929434 | D4 | semidirect |
| 84. #11929434 | C2×D4 | semidirect |
| 117. C2×C157 | #468 | semidirect |
| 123. C157 | C2×#468 | semidirect |
| 131. C2×#103 | D157 | semidirect |
| 153. #103 | C2×D157 | semidirect |
| 243. C2 | #23757522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| C22×#14578937 | 2 |
| C2×#19097747 | 2 |
| C2×#19097746 | 2 |
| #23757522 | 2 |
| C2×#19097704 | 2 |
| C2×#19097693 | 2 |
| C2×#103×C157 | 2 |
| C2×#468 | 157 |