Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19097796 | C2 | semidirect |
| 2. C22×#14578941 | C2 | semidirect |
| 3. #23757837 | C2 | semidirect |
| 4. #23757418 | C2 | semidirect |
| 5. #23757412 | C2 | semidirect |
| 6. #23757282 | C2 | semidirect |
| 7. #23757269 | C2 | semidirect |
| 8. #23757240 | C2 | semidirect |
| 9. C2×2−1+4×C157 | C2 | semidirect |
| 23. #19097695 | C22 | semidirect |
| 24. #19097695 | C22 | semidirect |
| 25. #19097692 | C22 | semidirect |
| 26. C22⋊#11929434 | C22 | semidirect |
| 33. C2×#41×C157 | C22 | semidirect |
| 36. C22×Q8×C157 | C22 | semidirect |
| 61. #41×C157 | D4 | semidirect |
| 69. C2×Q8×C157 | D4 | semidirect |
| 145. C157 | #3010 | semidirect |
| 147. C2×2−1+4 | D157 | semidirect |
| 162. C2×#41 | C2×D157 | semidirect |
| 165. C22×Q8 | C2×D157 | semidirect |
| 191. #41 | C22⋊D157 | semidirect |
| 199. C2×Q8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097796 | 2 |
| C22×#14578941 | 2 |
| #23757837 | 2 |
| #23757418 | 2 |
| #23757412 | 2 |
| #23757282 | 2 |
| #23757269 | 2 |
| #23757240 | 2 |
| C2×2−1+4×C157 | 2 |
| #3010 | 157 |