Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757830 | C2 | semidirect |
| 3. #23757609 | C2 | semidirect |
| 4. #23757554 | C2 | semidirect |
| 5. #23757479 | C2 | semidirect |
| 7. #23757375 | C2 | semidirect |
| 8. #432×C157 | C2 | semidirect |
| 12. #19097771 | C22 | semidirect |
| 13. #19097771 | C22 | semidirect |
| 18. C4×Dic314 | C22 | semidirect |
| 26. #19097705 | C22 | semidirect |
| 27. #19097696 | C22 | semidirect |
| 30. C4⋊C8×C157 | C22 | semidirect |
| 32. #97×C157 | C22 | semidirect |
| 112. C157 | #3110 | semidirect |
| 121. #432 | D157 | semidirect |
| 141. C4⋊C8 | C2×D157 | semidirect |
| 145. #97 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| C2×C4×D628 | 2 |
| #23757609 | 2 |
| #23757554 | 2 |
| #23757479 | 2 |
| #23757426 | 2 |
| #23757375 | 2 |
| #432×C157 | 2 |
| #3110 | 157 |