Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27161096 | C2 | semidirect |
| 3. #27161085 | C2 | semidirect |
| 4. C2×#20263242 | C2 | semidirect |
| 5. #27160851 | C2 | semidirect |
| 6. #27160837 | C2 | semidirect |
| 7. #568×C197 | C2 | semidirect |
| 11. C2×#15691345 | C4 | semidirect |
| 12. C2×#15691343 | C4 | semidirect |
| 112. C197 | #1903 | semidirect |
| 115. #568 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| #27161096 | 2 |
| #27161085 | 2 |
| C2×#20263242 | 2 |
| #27160851 | 2 |
| #27160837 | 2 |
| #568×C197 | 2 |
| #1903 | 197 |