Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #23757879 | C2 | direct (N × H) |
| 2. C2×#19097768 | C2 | semidirect |
| 3. C2×#19097756 | C2 | semidirect |
| 4. C2×#19097746 | C2 | semidirect |
| 5. C2×#19097746 | C2 | semidirect |
| 6. C2×#19097733 | C2 | semidirect |
| 7. C2×#19097728 | C2 | semidirect |
| 8. C2×#125×C157 | C2 | semidirect |
| 14. #19097768 | C22 | semidirect |
| 15. #19097756 | C22 | semidirect |
| 16. #19097746 | C22 | semidirect |
| 17. #19097746 | C22 | semidirect |
| 18. #19097733 | C22 | semidirect |
| 19. #19097728 | C22 | semidirect |
| 25. #125×C157 | C22 | semidirect |
| 92. C2×C157 | #540 | semidirect |
| 97. C157 | C2×#540 | semidirect |
| 101. C2×#125 | D157 | semidirect |
| 113. #125 | C2×D157 | semidirect |
| 192. C2 | #23757879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757879 | 2 |
| C2×#19097768 | 2 |
| C2×#19097756 | 2 |
| C2×#19097746 | 2 |
| C2×#19097733 | 2 |
| C2×#19097728 | 2 |
| C2×#125×C157 | 2 |
| C2×#540 | 157 |