Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#20263352 | C2 | semidirect |
| 2. C2×#20263348 | C2 | semidirect |
| 3. #27161646 | C2 | semidirect |
| 4. #27161560 | C2 | semidirect |
| 5. #27161300 | C2 | semidirect |
| 6. #27161293 | C2 | semidirect |
| 7. #27161278 | C2 | semidirect |
| 8. #27161273 | C2 | semidirect |
| 9. #27161105 | C2 | semidirect |
| 10. #27161078 | C2 | semidirect |
| 11. C2×#102×C197 | C2 | semidirect |
| 16. C2×Dic788 | C22 | semidirect |
| 17. C2×#15691347 | C22 | semidirect |
| 18. C2×#15691347 | C22 | semidirect |
| 20. C2×D1576 | C22 | semidirect |
| 28. #20263291 | C22 | semidirect |
| 29. #20263288 | C22 | semidirect |
| 34. #20263255 | C22 | semidirect |
| 35. #20263255 | C22 | semidirect |
| 36. #20263249 | C22 | semidirect |
| 37. #20263246 | C22 | semidirect |
| 46. #15691358 | D4 | semidirect |
| 154. C197 | #3045 | semidirect |
| 166. C2×#102 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| C2×#20263348 | 2 |
| #27161646 | 2 |
| #27161560 | 2 |
| #27161300 | 2 |
| #27161293 | 2 |
| #27161278 | 2 |
| #27161273 | 2 |
| #27161105 | 2 |
| #27161078 | 2 |
| C2×#102×C197 | 2 |
| #3045 | 197 |