Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20263326 | C2 | semidirect |
| 5. #27161263 | C2 | direct (N × H) |
| 6. C2×#20263254 | C2 | semidirect |
| 7. C2×#20263244 | C2 | semidirect |
| 8. C2×#104×C197 | C2 | semidirect |
| 22. #20263359 | C22 | semidirect |
| 24. #20263356 | C22 | semidirect |
| 31. #20263326 | C22 | semidirect |
| 33. #20263254 | C22 | semidirect |
| 34. #20263244 | C22 | semidirect |
| 38. #104×C197 | C22 | semidirect |
| 167. C2×C197 | #456 | semidirect |
| 170. C197 | C2×#456 | semidirect |
| 178. C2×#104 | D197 | semidirect |
| 208. #104 | C2×D197 | semidirect |
| 339. C2 | #27161263 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| C2×#20263359 | 2 |
| C2×#20263356 | 2 |
| C2×#20263326 | 2 |
| #27161263 | 2 |
| C2×#20263254 | 2 |
| C2×#20263244 | 2 |
| C2×#104×C197 | 2 |
| C2×#456 | 197 |