Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #23758039 | C2 | semidirect |
| 3. #23757396 | C2 | semidirect |
| 4. #23757391 | C2 | semidirect |
| 5. #23757322 | C2 | semidirect |
| 6. C2×#19097699 | C2 | semidirect |
| 7. C4×M16×C157 | C2 | semidirect |
| 9. #19097804 | C4 | semidirect |
| 10. #19097799 | C4 | semidirect |
| 13. #19097777 | C22 | semidirect |
| 16. #19097707 | C22 | semidirect |
| 17. #19097699 | C22 | semidirect |
| 18. #19097699 | C22 | semidirect |
| 22. #97×C157 | C22 | semidirect |
| 23. C4×C8×C157 | C22 | semidirect |
| 32. Dic628 | C2×C4 | semidirect |
| 33. #14578943 | C2×C4 | semidirect |
| 34. D1256 | C2×C4 | semidirect |
| 85. C157 | #2956 | semidirect |
| 93. C4×M16 | D157 | semidirect |
| 108. #97 | C2×D157 | semidirect |
| 109. C4×C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758073 | 2 |
| #23758039 | 2 |
| #23757396 | 2 |
| #23757391 | 2 |
| #23757322 | 2 |
| C2×#19097699 | 2 |
| C4×M16×C157 | 2 |
| #2956 | 157 |