Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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. C22×#15691348 | C2 | semidirect |
| 4. #27161655 | C2 | semidirect |
| 5. #27161244 | C2 | semidirect |
| 6. #27161236 | C2 | semidirect |
| 7. #27161073 | C2 | semidirect |
| 8. #27161047 | C2 | semidirect |
| 9. #419×C197 | C2 | semidirect |
| 140. C197 | #3011 | semidirect |
| 148. #419 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263374 | 2 |
| C2×#20263359 | 2 |
| C22×#15691348 | 2 |
| #27161655 | 2 |
| #27161244 | 2 |
| #27161236 | 2 |
| #27161073 | 2 |
| #27161047 | 2 |
| #419×C197 | 2 |
| #3011 | 197 |