Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#19097797 | C2 | semidirect |
| 2. C2×#19097793 | C2 | semidirect |
| 3. #23757840 | C2 | semidirect |
| 4. #23757661 | C2 | semidirect |
| 5. #23757656 | C2 | semidirect |
| 6. #23757648 | C2 | semidirect |
| 7. #23757228 | C2 | semidirect |
| 8. C22×D8×C157 | C2 | semidirect |
| 12. C2×Dic628 | C22 | semidirect |
| 13. C2×#14578943 | C22 | semidirect |
| 14. C2×#14578942 | C22 | semidirect |
| 15. C2×D1256 | C22 | semidirect |
| 16. C2×#14578939 | C22 | semidirect |
| 18. #19097767 | C22 | semidirect |
| 19. #19097758 | C22 | semidirect |
| 23. #19097681 | C22 | semidirect |
| 24. C8×Dic157 | C22 | semidirect |
| 42. #14578938 | D4 | semidirect |
| 56. C2×C8×C157 | D4 | semidirect |
| 101. C157 | #3155 | semidirect |
| 105. C22×D8 | D157 | semidirect |
| 154. 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×#19097797 | 2 |
| C2×#19097793 | 2 |
| #23757840 | 2 |
| #23757661 | 2 |
| #23757656 | 2 |
| #23757648 | 2 |
| #23757228 | 2 |
| C22×D8×C157 | 2 |
| #3155 | 157 |