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×#19097818 | C2 | semidirect |
| 2. C2×#19097804 | C2 | semidirect |
| 3. C2×#19097791 | C2 | semidirect |
| 4. #23757854 | C2 | semidirect |
| 5. #23757436 | C2 | semidirect |
| 6. #23757430 | C2 | semidirect |
| 7. #23757419 | C2 | semidirect |
| 8. #23757413 | C2 | semidirect |
| 9. C2×#19097694 | C2 | semidirect |
| 10. #23757241 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 58. C2×Dic314 | D4 | semidirect |
| 87. #41×C157 | D4 | semidirect |
| 169. C157 | #3013 | semidirect |
| 179. #417 | D157 | semidirect |
| 224. #41 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097818 | 2 |
| C2×#19097804 | 2 |
| C2×#19097791 | 2 |
| #23757854 | 2 |
| #23757436 | 2 |
| #23757430 | 2 |
| #23757419 | 2 |
| #23757413 | 2 |
| C2×#19097694 | 2 |
| #23757241 | 2 |
| #417×C157 | 2 |
| #3013 | 157 |