Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. C2×#20263373 | C2 | semidirect |
| 2. #27161879 | C2 | semidirect |
| 3. #27161877 | C2 | semidirect |
| 4. #27161655 | C2 | semidirect |
| 5. #27161263 | C2 | semidirect |
| 6. #27161253 | C2 | semidirect |
| 7. #27161097 | C2 | semidirect |
| 8. C2×#20263244 | C2 | semidirect |
| 9. #421×C197 | C2 | semidirect |
| 23. #20263359 | C22 | semidirect |
| 25. #20263356 | C22 | semidirect |
| 27. #20263354 | C22 | semidirect |
| 29. #20263351 | C22 | semidirect |
| 33. #20263326 | C22 | semidirect |
| 34. #20263314 | C22 | semidirect |
| 37. #20263254 | C22 | semidirect |
| 38. #20263244 | C22 | semidirect |
| 42. #104×C197 | C22 | semidirect |
| 185. C197 | #3020 | semidirect |
| 194. #421 | D197 | semidirect |
| 227. #104 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| #27161879 | 2 |
| #27161877 | 2 |
| #27161655 | 2 |
| #27161263 | 2 |
| #27161253 | 2 |
| #27161097 | 2 |
| C2×#20263244 | 2 |
| #421×C197 | 2 |
| #3020 | 197 |