Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1144 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 3. #23757135 | C2 | direct (N × H) |
| 4. C2×#19097678 | C2 | semidirect |
| 5. C2×#19097678 | C2 | semidirect |
| 6. C2×#95×C157 | C2 | semidirect |
| 11. C22×C4×D157 | C4 | semidirect |
| 15. #19097678 | C22 | semidirect |
| 16. #19097678 | C22 | semidirect |
| 19. #95×C157 | C22 | semidirect |
| 35. C2×C4×D157 | C2×C4 | semidirect |
| 96. C2×C157 | #381 | semidirect |
| 103. C157 | C2×#381 | semidirect |
| 110. C2×#95 | D157 | semidirect |
| 123. #95 | C2×D157 | semidirect |
| 201. C2 | #23757135 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D157 | 2 |
| C22×#14578931 | 2 |
| #23757135 | 2 |
| C2×#19097678 | 2 |
| C2×#95×C157 | 2 |
| C2×#381 | 157 |