Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20263351 | C2 | semidirect |
| 2. C22×#15691343 | C2 | semidirect |
| 3. #27161553 | C2 | semidirect |
| 4. #27161291 | C2 | semidirect |
| 5. #27161271 | C2 | semidirect |
| 6. #27161106 | C2 | semidirect |
| 7. #27161084 | C2 | semidirect |
| 8. #27161075 | C2 | semidirect |
| 9. #535×C197 | C2 | semidirect |
| 12. C2×#15691345 | C22 | semidirect |
| 15. C2×#15691343 | C22 | semidirect |
| 18. C4×D788 | C22 | semidirect |
| 22. C4⋊#13096802 | C22 | semidirect |
| 23. #20263250 | C22 | semidirect |
| 24. #20263247 | C22 | semidirect |
| 25. #20263247 | C22 | semidirect |
| 28. #127×C197 | C22 | semidirect |
| 29. #124×C197 | C22 | semidirect |
| 36. C2×D788 | D4 | semidirect |
| 121. C197 | #3041 | semidirect |
| 125. #535 | D197 | semidirect |
| 142. #127 | C2×D197 | semidirect |
| 143. #124 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C22×#15691343 | 2 |
| #27161553 | 2 |
| #27161291 | 2 |
| #27161271 | 2 |
| #27161106 | 2 |
| #27161084 | 2 |
| #27161075 | 2 |
| #535×C197 | 2 |
| #3041 | 197 |