Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23757173 | C2 | semidirect |
| 3. #23757167 | C2 | semidirect |
| 4. #23757161 | C2 | semidirect |
| 5. #23757149 | C2 | semidirect |
| 6. #23757129 | C2 | semidirect |
| 7. #379×C157 | C2 | semidirect |
| 9. C22×C4×D157 | C22 | semidirect |
| 10. #19097740 | C4 | semidirect |
| 11. C2×#14578933 | C22 | semidirect |
| 15. C2×#14578931 | C22 | semidirect |
| 16. C2×C4×Dic157 | C22 | semidirect |
| 17. #19097678 | C22 | semidirect |
| 18. #19097678 | C22 | semidirect |
| 33. C22⋊Dic157 | C2×C4 | semidirect |
| 38. C24×C157 | C2×C4 | semidirect |
| 95. C157 | #2375 | semidirect |
| 103. #379 | D157 | semidirect |
| 121. C24 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097740 | 2 |
| #23757173 | 2 |
| #23757167 | 2 |
| #23757161 | 2 |
| #23757149 | 2 |
| #23757129 | 2 |
| #379×C157 | 2 |
| #2375 | 157 |