Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×#20263345 | C2 | semidirect |
| 2. C22×Dic788 | C2 | semidirect |
| 3. #27161735 | C2 | semidirect |
| 4. #27161462 | C2 | semidirect |
| 5. #27161321 | C2 | semidirect |
| 6. #27161300 | C2 | semidirect |
| 7. #27161242 | C2 | semidirect |
| 8. #27161217 | C2 | semidirect |
| 9. #27161173 | C2 | semidirect |
| 10. C8×C22⋊D197 | C2 | semidirect |
| 11. #466×C197 | C2 | semidirect |
| 55. Dic788 | D4 | semidirect |
| 116. C22×C197 | #135 | semidirect |
| 136. C197 | #3285 | semidirect |
| 143. #466 | D197 | semidirect |
| 256. C22 | #20263345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263345 | 2 |
| C22×Dic788 | 2 |
| #27161735 | 2 |
| #27161462 | 2 |
| #27161321 | 2 |
| #27161300 | 2 |
| #27161242 | 2 |
| #27161217 | 2 |
| #27161173 | 2 |
| C8×C22⋊D197 | 2 |
| #466×C197 | 2 |
| #3285 | 197 |