Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 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×Q8×D157 | C2 | semidirect |
| 2. C2×#19097804 | C2 | semidirect |
| 3. C2×#19097802 | C2 | semidirect |
| 5. #23757430 | C2 | semidirect |
| 6. #23757413 | C2 | semidirect |
| 7. #23757281 | C2 | semidirect |
| 8. #23757236 | C2 | semidirect |
| 9. #419×C157 | C2 | semidirect |
| 21. C2×Dic628 | C22 | semidirect |
| 22. C2×#14578944 | C22 | semidirect |
| 23. C2×#14578943 | C22 | semidirect |
| 24. C2×#14578941 | C22 | semidirect |
| 31. #19097694 | C22 | semidirect |
| 36. #103×C157 | C22 | semidirect |
| 44. C2×Dic314 | D4 | semidirect |
| 73. C2×Q8×C157 | D4 | semidirect |
| 127. C2×D157 | #137 | semidirect |
| 141. C157 | #3004 | semidirect |
| 150. #419 | D157 | semidirect |
| 177. #103 | C2×D157 | semidirect |
| 194. C2×Q8 | D628 | 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×#19097804 | 2 |
| C2×#19097802 | 2 |
| #23757785 | 2 |
| #23757430 | 2 |
| #23757413 | 2 |
| #23757281 | 2 |
| #23757236 | 2 |
| #419×C157 | 2 |
| #3004 | 157 |