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×#19097796 | C2 | semidirect |
| 3. C2×#19097791 | C2 | semidirect |
| 4. C22×#14578941 | C2 | semidirect |
| 5. #23757842 | C2 | semidirect |
| 6. #23757665 | C2 | semidirect |
| 7. #23757663 | C2 | semidirect |
| 8. #23757655 | C2 | semidirect |
| 9. #23757647 | C2 | semidirect |
| 10. #23757229 | C2 | semidirect |
| 11. #536×C157 | C2 | semidirect |
| 17. C2×#14578944 | C22 | semidirect |
| 18. C2×#14578944 | C22 | semidirect |
| 19. C2×#14578942 | C22 | semidirect |
| 24. C2×#14578941 | C22 | semidirect |
| 25. C2×#14578941 | C22 | semidirect |
| 27. C2×#14578939 | C22 | semidirect |
| 34. #19097682 | C22 | semidirect |
| 35. C4×#11929434 | C22 | semidirect |
| 38. C4⋊Q8×C157 | C22 | semidirect |
| 39. #124×C157 | C22 | semidirect |
| 65. #14578938 | D4 | semidirect |
| 66. C2×#11929434 | D4 | semidirect |
| 148. C157 | #3154 | semidirect |
| 154. #536 | D157 | semidirect |
| 181. C4⋊Q8 | C2×D157 | semidirect |
| 184. #124 | C2×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×#19097796 | 2 |
| C2×#19097791 | 2 |
| C22×#14578941 | 2 |
| #23757842 | 2 |
| #23757665 | 2 |
| #23757663 | 2 |
| #23757655 | 2 |
| #23757647 | 2 |
| #23757229 | 2 |
| #536×C157 | 2 |
| #3154 | 157 |