Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097802 | C2 | semidirect |
| 2. C2×#19097797 | C2 | semidirect |
| 3. C2×#19097793 | C2 | semidirect |
| 4. #23757847 | C2 | semidirect |
| 5. #23757840 | C2 | semidirect |
| 6. #23757664 | C2 | semidirect |
| 7. #23757659 | C2 | semidirect |
| 8. #23757654 | C2 | semidirect |
| 9. #23757644 | C2 | semidirect |
| 10. #23757228 | C2 | semidirect |
| 11. C22×SD16×C157 | C2 | semidirect |
| 17. C2×Dic628 | C22 | semidirect |
| 18. C2×#14578944 | C22 | semidirect |
| 19. C2×#14578943 | C22 | semidirect |
| 20. C2×#14578943 | C22 | semidirect |
| 22. C2×#14578941 | C22 | semidirect |
| 23. C2×D1256 | C22 | semidirect |
| 26. #19097769 | C22 | semidirect |
| 28. #19097760 | C22 | semidirect |
| 35. #19097681 | C22 | semidirect |
| 36. C8×Dic157 | C22 | semidirect |
| 64. #14578938 | D4 | semidirect |
| 85. C2×C8×C157 | D4 | semidirect |
| 148. C157 | #3154 | semidirect |
| 153. C22×SD16 | D157 | semidirect |
| 228. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| C2×#19097797 | 2 |
| C2×#19097793 | 2 |
| #23757847 | 2 |
| #23757840 | 2 |
| #23757664 | 2 |
| #23757659 | 2 |
| #23757654 | 2 |
| #23757644 | 2 |
| #23757228 | 2 |
| C22×SD16×C157 | 2 |
| #3154 | 157 |