Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27160979 | C2 | semidirect |
| 3. #27160973 | C2 | semidirect |
| 4. #27160967 | C2 | semidirect |
| 5. #27160955 | C2 | semidirect |
| 6. #27160935 | C2 | semidirect |
| 7. #379×C197 | C2 | semidirect |
| 9. C22×C4×D197 | C22 | semidirect |
| 10. #20263295 | C4 | semidirect |
| 11. C2×#15691337 | C22 | semidirect |
| 15. C2×#15691335 | C22 | semidirect |
| 16. C2×C4×Dic197 | C22 | semidirect |
| 17. #20263233 | C22 | semidirect |
| 18. #20263233 | C22 | semidirect |
| 33. C22⋊Dic197 | C2×C4 | semidirect |
| 38. C24×C197 | C2×C4 | semidirect |
| 95. C197 | #2375 | semidirect |
| 103. #379 | D197 | semidirect |
| 121. C24 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263295 | 2 |
| #27160979 | 2 |
| #27160973 | 2 |
| #27160967 | 2 |
| #27160955 | 2 |
| #27160935 | 2 |
| #379×C197 | 2 |
| #2375 | 197 |