Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19097779 | C2 | semidirect |
| 3. #23757847 | C2 | semidirect |
| 5. #23757522 | C2 | semidirect |
| 6. #23757505 | C2 | semidirect |
| 7. #23757309 | C2 | semidirect |
| 8. #23757279 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 16. C2×#14578937 | C22 | semidirect |
| 18. C2×C8×D157 | C22 | semidirect |
| 24. #19097747 | C22 | semidirect |
| 28. #19097704 | C22 | semidirect |
| 29. #19097702 | C22 | semidirect |
| 34. #103×C157 | C22 | semidirect |
| 50. C2×#11929434 | D4 | semidirect |
| 120. C157 | #3057 | semidirect |
| 129. #419 | D157 | semidirect |
| 154. #103 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578941 | 2 |
| C2×#19097779 | 2 |
| #23757847 | 2 |
| #23757842 | 2 |
| #23757522 | 2 |
| #23757505 | 2 |
| #23757309 | 2 |
| #23757279 | 2 |
| #419×C157 | 2 |
| #3057 | 157 |