Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20263359 | C2 | semidirect |
| 3. C2×#20263313 | C2 | semidirect |
| 4. #27161547 | C2 | semidirect |
| 5. #27161300 | C2 | semidirect |
| 6. #27161293 | C2 | semidirect |
| 7. #27161102 | C2 | semidirect |
| 8. #27161087 | C2 | semidirect |
| 9. #418×C197 | C2 | semidirect |
| 14. C2×Dic788 | C22 | semidirect |
| 15. C2×#15691347 | C22 | semidirect |
| 22. #20263291 | C22 | semidirect |
| 23. #20263288 | C22 | semidirect |
| 29. #20263255 | C22 | semidirect |
| 30. #20263249 | C22 | semidirect |
| 125. C197 | #3040 | semidirect |
| 135. #418 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263359 | 2 |
| C2×#20263352 | 2 |
| C2×#20263313 | 2 |
| #27161547 | 2 |
| #27161300 | 2 |
| #27161293 | 2 |
| #27161102 | 2 |
| #27161087 | 2 |
| #418×C197 | 2 |
| #3040 | 197 |