Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#14578954 | C2 | semidirect |
| 2. C2×#19097797 | C2 | semidirect |
| 3. #23757416 | C2 | semidirect |
| 4. #23757411 | C2 | semidirect |
| 5. #23757406 | C2 | semidirect |
| 6. #23757272 | C2 | semidirect |
| 7. #23757237 | C2 | semidirect |
| 8. C2×#121×C157 | C2 | semidirect |
| 13. C2×#14578954 | C22 | semidirect |
| 14. C22×Dic314 | C22 | semidirect |
| 15. C22×D628 | C22 | semidirect |
| 19. C2×#14578942 | C22 | semidirect |
| 20. C2×#14578939 | C22 | semidirect |
| 21. C2×#14578938 | C22 | semidirect |
| 22. #19097694 | C22 | semidirect |
| 23. #19097691 | C22 | semidirect |
| 24. C22⋊#11929434 | C22 | semidirect |
| 25. C22⋊#11929434 | C22 | semidirect |
| 27. C22×D4×C157 | C22 | semidirect |
| 32. #121×C157 | C22 | semidirect |
| 33. C2×C4⋊C4×C157 | C22 | semidirect |
| 41. #14578954 | D4 | semidirect |
| 85. Dic314 | C2×D4 | semidirect |
| 88. D628 | C2×D4 | semidirect |
| 135. C22×C157 | AGL(1,ℤ/8) | semidirect |
| 155. C157 | #3006 | semidirect |
| 159. C2×#121 | D157 | semidirect |
| 174. C22×D4 | C2×D157 | semidirect |
| 184. #121 | C2×D157 | semidirect |
| 185. C2×C4⋊C4 | C2×D157 | semidirect |
| 295. C22 | #19097797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578954 | 2 |
| C2×#19097797 | 2 |
| #23757416 | 2 |
| #23757411 | 2 |
| #23757406 | 2 |
| #23757272 | 2 |
| #23757237 | 2 |
| C2×#121×C157 | 2 |
| #3006 | 157 |