Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19097795 | C2 | semidirect |
| 2. #23757821 | C2 | semidirect |
| 3. C4×D4×D157 | C2 | semidirect |
| 4. #23757487 | C2 | semidirect |
| 5. #23757486 | C2 | semidirect |
| 6. #23757479 | C2 | semidirect |
| 7. #23757478 | C2 | semidirect |
| 8. #23757465 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 10. #23757271 | C2 | semidirect |
| 11. #459×C157 | C2 | semidirect |
| 20. #19097771 | C22 | semidirect |
| 21. #19097758 | C22 | semidirect |
| 34. C4⋊#11929434 | C22 | semidirect |
| 35. #19097700 | C22 | semidirect |
| 36. #19097696 | C22 | semidirect |
| 37. #19097694 | C22 | semidirect |
| 38. #19097692 | C22 | semidirect |
| 40. #127×C157 | C22 | semidirect |
| 42. C4⋊C8×C157 | C22 | semidirect |
| 43. #102×C157 | C22 | semidirect |
| 52. D4×D157 | D4 | semidirect |
| 145. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 160. C157 | #3036 | semidirect |
| 170. #459 | D157 | semidirect |
| 183. #127 | C2×D157 | semidirect |
| 200. C4⋊C8 | C2×D157 | semidirect |
| 204. #102 | C2×D157 | semidirect |
| 311. C4 | #19097795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097795 | 2 |
| #23757821 | 2 |
| C4×D4×D157 | 2 |
| #23757487 | 2 |
| #23757486 | 2 |
| #23757479 | 2 |
| #23757478 | 2 |
| #23757465 | 2 |
| #23757295 | 2 |
| #23757271 | 2 |
| #459×C157 | 2 |
| #3036 | 157 |