Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19097797 | C2 | semidirect |
| 2. #23757823 | C2 | semidirect |
| 3. #23757660 | C2 | semidirect |
| 4. #23757649 | C2 | semidirect |
| 5. #23757645 | C2 | semidirect |
| 6. C4×#14578938 | C2 | semidirect |
| 7. C2×#127×C157 | C2 | semidirect |
| 10. C2×#14578942 | C22 | semidirect |
| 11. C2×#14578939 | C22 | semidirect |
| 13. #19097771 | C22 | semidirect |
| 14. #19097768 | C22 | semidirect |
| 15. #19097759 | C22 | semidirect |
| 18. #19097682 | C22 | semidirect |
| 19. C4×#11929434 | C22 | semidirect |
| 34. #14578938 | D4 | semidirect |
| 57. #11929434 | C2×D4 | semidirect |
| 82. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 90. C157 | #3151 | semidirect |
| 94. C2×#127 | D157 | semidirect |
| 174. C4 | #19097797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097797 | 2 |
| #23757823 | 2 |
| #23757660 | 2 |
| #23757649 | 2 |
| #23757645 | 2 |
| C4×#14578938 | 2 |
| C2×#127×C157 | 2 |
| #3151 | 157 |