Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19097804 | C2 | semidirect |
| 2. C2×#19097801 | C2 | semidirect |
| 4. C2×#19097736 | C2 | semidirect |
| 5. #23757498 | C2 | semidirect |
| 6. #23757494 | C2 | semidirect |
| 7. #23757482 | C2 | semidirect |
| 8. #23757472 | C2 | semidirect |
| 9. #23757296 | C2 | semidirect |
| 10. #23757272 | C2 | semidirect |
| 11. #417×C157 | C2 | semidirect |
| 49. C2×Dic314 | D4 | semidirect |
| 150. Dic157 | #137 | semidirect |
| 157. C157 | #3037 | semidirect |
| 169. #417 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097801 | 2 |
| #23757819 | 2 |
| C2×#19097736 | 2 |
| #23757498 | 2 |
| #23757494 | 2 |
| #23757482 | 2 |
| #23757472 | 2 |
| #23757296 | 2 |
| #23757272 | 2 |
| #417×C157 | 2 |
| #3037 | 157 |