Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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×#19097729 | C2 | semidirect |
| 3. C2×#19097728 | C2 | semidirect |
| 4. #23757176 | C2 | semidirect |
| 5. #23757175 | C2 | semidirect |
| 6. #23757174 | C2 | semidirect |
| 7. #23757173 | C2 | semidirect |
| 8. #23757128 | C2 | semidirect |
| 9. #390×C157 | C2 | semidirect |
| 15. C2×D4×D157 | C4 | semidirect |
| 19. C2×C4⋊Dic157 | C22 | semidirect |
| 20. C2×#14578933 | C22 | semidirect |
| 21. C2×C22⋊Dic157 | C22 | semidirect |
| 24. C2×#14578931 | C22 | semidirect |
| 25. C2×#14578931 | C22 | semidirect |
| 26. C2×C4×Dic157 | C22 | semidirect |
| 27. C2×C4×Dic157 | C22 | semidirect |
| 29. C2×C4⋊C4×C157 | C22 | semidirect |
| 30. C2×C22⋊C4×C157 | C22 | semidirect |
| 31. C2×C42×C157 | C22 | semidirect |
| 96. C4×D157 | C22⋊C4 | semidirect |
| 147. C157 | #2309 | semidirect |
| 156. #390 | D157 | semidirect |
| 170. C2×C4⋊C4 | C2×D157 | semidirect |
| 176. C2×C22⋊C4 | C2×D157 | semidirect |
| 179. C2×C42 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D157 | 2 |
| C2×#19097729 | 2 |
| C2×#19097728 | 2 |
| #23757176 | 2 |
| #23757175 | 2 |
| #23757174 | 2 |
| #23757173 | 2 |
| #23757128 | 2 |
| #390×C157 | 2 |
| #2309 | 157 |