Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19097794 | C2 | semidirect |
| 2. C2×D8×D157 | C2 | semidirect |
| 3. #23757710 | C2 | direct (N × H) |
| 4. C2×#19097714 | C2 | semidirect |
| 5. C2×D2512 | C2 | semidirect |
| 6. C2×#19097712 | C2 | semidirect |
| 7. C2×#19097710 | C2 | semidirect |
| 8. C2×SD32×C157 | C2 | semidirect |
| 12. #19097794 | C22 | semidirect |
| 15. C2×D1256 | C22 | semidirect |
| 18. D8×D157 | C22 | semidirect |
| 20. #19097714 | C22 | semidirect |
| 21. D2512 | C22 | semidirect |
| 22. #19097712 | C22 | semidirect |
| 23. #19097710 | C22 | semidirect |
| 24. C2×#14578929 | C22 | semidirect |
| 25. C2×Q16×C157 | C22 | semidirect |
| 27. SD32×C157 | C22 | semidirect |
| 28. C2×C16×C157 | C22 | semidirect |
| 44. D1256 | C23 | semidirect |
| 49. #14578929 | C23 | semidirect |
| 53. Q16×C157 | C23 | semidirect |
| 57. C16×C157 | C23 | semidirect |
| 98. C2×C157 | #509 | semidirect |
| 103. C157 | C2×#509 | semidirect |
| 109. C2×SD32 | D157 | semidirect |
| 117. C2×Q16 | C2×D157 | semidirect |
| 127. SD32 | C2×D157 | semidirect |
| 132. C2×C16 | C2×D157 | semidirect |
| 147. Q16 | C22×D157 | semidirect |
| 161. C16 | C22×D157 | semidirect |
| 205. C2 | #23757710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×D8×D157 | 2 |
| #23757710 | 2 |
| C2×#19097714 | 2 |
| C2×D2512 | 2 |
| C2×#19097712 | 2 |
| C2×#19097710 | 2 |
| C2×SD32×C157 | 2 |
| C2×#509 | 157 |