Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097819 | C2 | semidirect |
| 2. C2×#19097791 | C2 | semidirect |
| 3. #23757851 | C2 | semidirect |
| 4. #23757434 | C2 | semidirect |
| 5. #23757427 | C2 | semidirect |
| 6. #23757417 | C2 | semidirect |
| 7. #23757410 | C2 | semidirect |
| 8. #23757275 | C2 | semidirect |
| 9. C2×#19097695 | C2 | semidirect |
| 10. #23757241 | C2 | semidirect |
| 11. C2×#137×C157 | C2 | semidirect |
| 52. #14578954 | D4 | semidirect |
| 86. C2×Q8×C157 | D4 | semidirect |
| 169. C157 | #3013 | semidirect |
| 172. C2×#137 | D157 | semidirect |
| 233. 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×#19097819 | 2 |
| C2×#19097791 | 2 |
| #23757851 | 2 |
| #23757434 | 2 |
| #23757427 | 2 |
| #23757417 | 2 |
| #23757410 | 2 |
| #23757275 | 2 |
| C2×#19097695 | 2 |
| #23757241 | 2 |
| C2×#137×C157 | 2 |
| #3013 | 157 |