Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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×#19097727 | C2 | semidirect |
| 3. #23757136 | C2 | semidirect |
| 4. #23757132 | C2 | semidirect |
| 6. #23757120 | C2 | semidirect |
| 7. #381×C157 | C2 | semidirect |
| 11. C22×C4×D157 | C4 | semidirect |
| 15. C2×#14578933 | C22 | semidirect |
| 18. C2×C4×Dic157 | C22 | semidirect |
| 19. #19097678 | C22 | semidirect |
| 22. #95×C157 | C22 | semidirect |
| 56. C2×Dic157 | C22⋊C4 | semidirect |
| 82. C2×D157 | #117 | semidirect |
| 93. C157 | #2280 | semidirect |
| 98. #381 | D157 | semidirect |
| 116. #95 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D157 | 2 |
| C2×#19097727 | 2 |
| #23757136 | 2 |
| #23757132 | 2 |
| #23757128 | 2 |
| #23757120 | 2 |
| #381×C157 | 2 |
| #2280 | 157 |