Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#20263359 | C2 | semidirect |
| 3. C2×#20263356 | C2 | semidirect |
| 4. #27161354 | C2 | semidirect |
| 5. #27161342 | C2 | semidirect |
| 6. #27161128 | C2 | semidirect |
| 7. #27161061 | C2 | semidirect |
| 8. C2×#20263244 | C2 | semidirect |
| 9. #568×C197 | C2 | semidirect |
| 21. C2×Dic788 | C22 | semidirect |
| 23. C2×#15691347 | C22 | semidirect |
| 27. #20263262 | C22 | semidirect |
| 28. #20263244 | C22 | semidirect |
| 29. #20263244 | C22 | semidirect |
| 30. #20263242 | C22 | semidirect |
| 142. C197 | #3069 | semidirect |
| 147. #568 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| C2×#20263359 | 2 |
| C2×#20263356 | 2 |
| #27161354 | 2 |
| #27161342 | 2 |
| #27161128 | 2 |
| #27161061 | 2 |
| C2×#20263244 | 2 |
| #568×C197 | 2 |
| #3069 | 197 |