Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15691347 | C2 | semidirect |
| 3. #27161655 | C2 | semidirect |
| 4. #27161553 | C2 | semidirect |
| 5. #27161295 | C2 | semidirect |
| 6. #27161285 | C2 | semidirect |
| 7. #27161089 | C2 | semidirect |
| 8. #27161076 | C2 | semidirect |
| 9. #424×C197 | C2 | semidirect |
| 18. #20263326 | C22 | semidirect |
| 19. #20263314 | C22 | semidirect |
| 26. #20263251 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 28. #20263248 | C22 | semidirect |
| 32. C4⋊C8×C197 | C22 | semidirect |
| 116. C197 | #3042 | semidirect |
| 124. #424 | D197 | semidirect |
| 146. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263354 | 2 |
| C22×#15691347 | 2 |
| #27161655 | 2 |
| #27161553 | 2 |
| #27161295 | 2 |
| #27161285 | 2 |
| #27161089 | 2 |
| #27161076 | 2 |
| #424×C197 | 2 |
| #3042 | 197 |