Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 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. C22×#15691346 | C2 | semidirect |
| 3. #27161655 | C2 | semidirect |
| 4. #27161294 | C2 | semidirect |
| 5. #27161284 | C2 | semidirect |
| 6. #27161106 | C2 | semidirect |
| 7. #27161087 | C2 | semidirect |
| 8. #27161073 | C2 | semidirect |
| 9. #518×C197 | C2 | semidirect |
| 19. #20263326 | C22 | semidirect |
| 20. #20263314 | C22 | semidirect |
| 23. C4⋊#13096802 | C22 | semidirect |
| 24. #20263249 | C22 | semidirect |
| 25. #20263249 | C22 | semidirect |
| 26. #20263246 | C22 | semidirect |
| 116. C197 | #3042 | semidirect |
| 121. #518 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| C22×#15691346 | 2 |
| #27161655 | 2 |
| #27161294 | 2 |
| #27161284 | 2 |
| #27161106 | 2 |
| #27161087 | 2 |
| #27161073 | 2 |
| #518×C197 | 2 |
| #3042 | 197 |