Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19097730 | C2 | semidirect |
| 3. #23757598 | C2 | semidirect |
| 4. #23757592 | C2 | semidirect |
| 5. #23757587 | C2 | semidirect |
| 6. #23757315 | C2 | semidirect |
| 7. #23757279 | C2 | semidirect |
| 8. #407×C157 | C2 | semidirect |
| 18. #19097730 | C22 | semidirect |
| 20. C2×C4⋊Dic157 | C22 | semidirect |
| 21. C2×C4⋊Dic157 | C22 | semidirect |
| 25. #19097705 | C22 | semidirect |
| 26. #19097703 | C22 | semidirect |
| 27. #19097693 | C22 | semidirect |
| 28. #19097693 | C22 | semidirect |
| 31. C22⋊C8×C157 | C22 | semidirect |
| 32. C22⋊C8×C157 | C22 | semidirect |
| 125. C157 | #3094 | semidirect |
| 134. #407 | D157 | semidirect |
| 157. C22⋊C8 | C2×D157 | semidirect |
| 158. C22⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097745 | 2 |
| C2×#19097730 | 2 |
| #23757598 | 2 |
| #23757592 | 2 |
| #23757587 | 2 |
| #23757315 | 2 |
| #23757279 | 2 |
| #407×C157 | 2 |
| #3094 | 157 |