Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097816 | C2 | semidirect |
| 2. C2×#19097799 | C2 | semidirect |
| 3. C2×#19097767 | C2 | semidirect |
| 4. #23757443 | C2 | direct (N × H) |
| 5. C2×#19097697 | C2 | semidirect |
| 6. C2×#100×C157 | C2 | semidirect |
| 9. #19097816 | C22 | semidirect |
| 12. C22×D628 | C22 | semidirect |
| 17. #19097799 | C22 | semidirect |
| 21. #19097767 | C22 | semidirect |
| 22. C2×C4×Dic157 | C22 | semidirect |
| 23. #19097697 | C22 | semidirect |
| 25. C2×M16×C157 | C22 | semidirect |
| 26. #100×C157 | C22 | semidirect |
| 31. #14578954 | D4 | semidirect |
| 35. C2×Dic314 | D4 | semidirect |
| 39. C2×D628 | D4 | semidirect |
| 40. C2×D628 | C23 | semidirect |
| 55. C4×Dic157 | C23 | semidirect |
| 63. M16×C157 | C23 | semidirect |
| 73. Dic314 | C2×D4 | semidirect |
| 77. D628 | C2×D4 | semidirect |
| 122. C2×C157 | #453 | semidirect |
| 126. C157 | C2×#453 | semidirect |
| 133. C2×#100 | D157 | semidirect |
| 148. C2×M16 | C2×D157 | semidirect |
| 153. #100 | C2×D157 | semidirect |
| 188. M16 | C22×D157 | semidirect |
| 251. C2 | #23757443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097816 | 2 |
| C2×#19097799 | 2 |
| C2×#19097767 | 2 |
| #23757443 | 2 |
| C2×#19097697 | 2 |
| C2×#100×C157 | 2 |
| C2×#453 | 157 |