Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D157 | C2 | semidirect |
| 2. C2×#19097800 | C2 | semidirect |
| 4. #23757431 | C2 | semidirect |
| 5. #23757430 | C2 | semidirect |
| 6. #23757429 | C2 | semidirect |
| 7. #23757411 | C2 | semidirect |
| 8. #23757410 | C2 | semidirect |
| 9. #23757280 | C2 | semidirect |
| 10. #23757235 | C2 | semidirect |
| 11. #448×C157 | C2 | semidirect |
| 23. C2×Dic628 | C22 | semidirect |
| 24. C2×#14578944 | C22 | semidirect |
| 25. C2×#14578942 | C22 | semidirect |
| 35. #19097696 | C22 | semidirect |
| 36. #19097695 | C22 | semidirect |
| 37. #19097694 | C22 | semidirect |
| 41. C2×SD16×C157 | C22 | semidirect |
| 43. #103×C157 | C22 | semidirect |
| 59. Q8×D157 | D4 | semidirect |
| 144. C22×C157 | #137 | semidirect |
| 152. C2×D157 | #137 | semidirect |
| 169. C157 | #3004 | semidirect |
| 179. #448 | D157 | semidirect |
| 197. C2×SD16 | C2×D157 | semidirect |
| 211. #103 | C2×D157 | semidirect |
| 321. C22 | #19097800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D157 | 2 |
| C2×#19097800 | 2 |
| #23757783 | 2 |
| #23757431 | 2 |
| #23757430 | 2 |
| #23757429 | 2 |
| #23757411 | 2 |
| #23757410 | 2 |
| #23757280 | 2 |
| #23757235 | 2 |
| #448×C157 | 2 |
| #3004 | 157 |