Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#20263324 | C2 | semidirect |
| 5. #27161288 | C2 | semidirect |
| 6. #27161283 | C2 | semidirect |
| 7. #27161102 | C2 | semidirect |
| 8. #27161087 | C2 | semidirect |
| 9. #419×C197 | C2 | semidirect |
| 116. Dic197 | #137 | semidirect |
| 121. C197 | #3039 | semidirect |
| 131. #419 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263359 | 2 |
| C2×#20263357 | 2 |
| C2×#20263324 | 2 |
| #27161547 | 2 |
| #27161288 | 2 |
| #27161283 | 2 |
| #27161102 | 2 |
| #27161087 | 2 |
| #419×C197 | 2 |
| #3039 | 197 |