Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic788 | C2 | semidirect |
| 3. C22×#15691347 | C2 | semidirect |
| 4. C2×#20263305 | C2 | semidirect |
| 5. #27161243 | C2 | direct (N × H) |
| 6. C2×#20263251 | C2 | semidirect |
| 7. C2×#20263248 | C2 | semidirect |
| 8. C2×C22⋊C8×C197 | C2 | semidirect |
| 19. C2×Dic788 | C22 | semidirect |
| 21. C2×#15691347 | C22 | semidirect |
| 23. #20263305 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 28. #20263248 | C22 | semidirect |
| 32. C22⋊C8×C197 | C22 | semidirect |
| 130. C2×C197 | #452 | semidirect |
| 135. C197 | C2×#452 | semidirect |
| 144. C2×C22⋊C8 | D197 | semidirect |
| 168. C22⋊C8 | C2×D197 | semidirect |
| 267. C2 | #27161243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C22×Dic788 | 2 |
| C22×#15691347 | 2 |
| C2×#20263305 | 2 |
| #27161243 | 2 |
| C2×#20263251 | 2 |
| C2×#20263248 | 2 |
| C2×C22⋊C8×C197 | 2 |
| C2×#452 | 197 |