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×#20263356 | C2 | semidirect |
| 3. C22×Dic788 | C2 | semidirect |
| 4. #27161655 | C2 | semidirect |
| 5. #27161242 | C2 | semidirect |
| 6. #27161236 | C2 | semidirect |
| 7. #27161087 | C2 | semidirect |
| 8. #27161045 | C2 | semidirect |
| 9. #416×C197 | C2 | semidirect |
| 140. C197 | #3011 | semidirect |
| 149. #416 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| C2×#20263356 | 2 |
| C22×Dic788 | 2 |
| #27161655 | 2 |
| #27161242 | 2 |
| #27161236 | 2 |
| #27161087 | 2 |
| #27161045 | 2 |
| #416×C197 | 2 |
| #3011 | 197 |