Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 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. C2×#19097793 | C2 | semidirect |
| 2. #23757703 | C2 | direct (N × H) |
| 3. C2×#19097717 | C2 | semidirect |
| 4. C2×#19097715 | C2 | semidirect |
| 5. C2×#19097714 | C2 | semidirect |
| 6. C2×#19097712 | C2 | semidirect |
| 7. C22×#14578929 | C2 | semidirect |
| 8. C2×#135×C157 | C2 | semidirect |
| 11. #19097793 | C22 | semidirect |
| 15. #19097717 | C22 | semidirect |
| 16. #19097715 | C22 | semidirect |
| 17. #19097714 | C22 | semidirect |
| 18. #19097712 | C22 | semidirect |
| 21. C2×#14578929 | C22 | semidirect |
| 24. #135×C157 | C22 | semidirect |
| 96. C2×C157 | #508 | semidirect |
| 99. C157 | C2×#508 | semidirect |
| 102. C2×#135 | D157 | semidirect |
| 114. #135 | C2×D157 | semidirect |
| 197. C2 | #23757703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| #23757703 | 2 |
| C2×#19097717 | 2 |
| C2×#19097715 | 2 |
| C2×#19097714 | 2 |
| C2×#19097712 | 2 |
| C22×#14578929 | 2 |
| C2×#135×C157 | 2 |
| C2×#508 | 157 |