Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 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×#14578939 | C2 | semidirect |
| 2. C2×#19097779 | C2 | semidirect |
| 3. #23757842 | C2 | semidirect |
| 4. #23757840 | C2 | semidirect |
| 5. #23757525 | C2 | semidirect |
| 6. #23757508 | C2 | semidirect |
| 7. #23757309 | C2 | semidirect |
| 8. #23757279 | C2 | semidirect |
| 9. #418×C157 | C2 | semidirect |
| 16. C2×#14578937 | C22 | semidirect |
| 18. C2×C8×D157 | C22 | semidirect |
| 23. #19097746 | C22 | semidirect |
| 24. #19097742 | C22 | semidirect |
| 28. #19097704 | C22 | semidirect |
| 29. #19097702 | C22 | semidirect |
| 30. #19097693 | C22 | semidirect |
| 34. #102×C157 | C22 | semidirect |
| 51. C2×#11929434 | D4 | semidirect |
| 125. C157 | #3058 | semidirect |
| 135. #418 | D157 | semidirect |
| 160. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578939 | 2 |
| C2×#19097779 | 2 |
| #23757842 | 2 |
| #23757840 | 2 |
| #23757525 | 2 |
| #23757508 | 2 |
| #23757309 | 2 |
| #23757279 | 2 |
| #418×C157 | 2 |
| #3058 | 157 |