Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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×#19097779 | C2 | semidirect |
| 2. C22×C8×D157 | C2 | semidirect |
| 4. #23757343 | C2 | semidirect |
| 5. #23757338 | C2 | semidirect |
| 6. #23757239 | C2 | semidirect |
| 7. #23757236 | C2 | semidirect |
| 8. #23757229 | C2 | semidirect |
| 9. #424×C157 | C2 | semidirect |
| 14. C2×#14578937 | C22 | semidirect |
| 19. C2×C8×D157 | C22 | semidirect |
| 26. #19097683 | C22 | semidirect |
| 27. #19097682 | C22 | semidirect |
| 28. C4×#11929434 | C22 | semidirect |
| 32. C4⋊C8×C157 | C22 | semidirect |
| 48. C2×#11929434 | D4 | semidirect |
| 101. C2×D157 | #131 | semidirect |
| 113. C157 | #2929 | semidirect |
| 120. #424 | D157 | semidirect |
| 142. C4⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097779 | 2 |
| C22×C8×D157 | 2 |
| #23757785 | 2 |
| #23757343 | 2 |
| #23757338 | 2 |
| #23757239 | 2 |
| #23757236 | 2 |
| #23757229 | 2 |
| #424×C157 | 2 |
| #2929 | 157 |