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×#19097802 | C2 | semidirect |
| 3. C2×#19097793 | C2 | semidirect |
| 4. #23757854 | C2 | semidirect |
| 5. #23757438 | C2 | semidirect |
| 6. #23757430 | C2 | semidirect |
| 7. #23757421 | C2 | semidirect |
| 8. #23757413 | C2 | semidirect |
| 9. #23757272 | C2 | semidirect |
| 10. #23757239 | C2 | semidirect |
| 11. C2×#103×C157 | C2 | semidirect |
| 54. #14578954 | D4 | semidirect |
| 88. C2×Q8×C157 | D4 | semidirect |
| 169. C157 | #3013 | semidirect |
| 180. C2×#103 | D157 | semidirect |
| 234. C2×Q8 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097819 | 2 |
| C2×#19097802 | 2 |
| C2×#19097793 | 2 |
| #23757854 | 2 |
| #23757438 | 2 |
| #23757430 | 2 |
| #23757421 | 2 |
| #23757413 | 2 |
| #23757272 | 2 |
| #23757239 | 2 |
| C2×#103×C157 | 2 |
| #3013 | 157 |