Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #27161634 | C2 | semidirect |
| 3. #27161442 | C2 | semidirect |
| 4. #27161427 | C2 | semidirect |
| 5. #27161426 | C2 | semidirect |
| 6. #27161425 | C2 | semidirect |
| 7. #27161082 | C2 | semidirect |
| 8. C4×#15691341 | C2 | semidirect |
| 9. #486×C197 | C2 | semidirect |
| 14. #20263326 | C22 | semidirect |
| 19. #20263317 | C22 | semidirect |
| 26. #20263248 | C22 | semidirect |
| 27. #20263247 | C22 | semidirect |
| 28. #20263246 | C22 | semidirect |
| 29. #20263236 | C22 | semidirect |
| 30. C4×#13096802 | C22 | semidirect |
| 31. C4⋊Q8×C197 | C22 | semidirect |
| 33. #102×C197 | C22 | semidirect |
| 34. C4×C8×C197 | C22 | semidirect |
| 123. C197 | #3138 | semidirect |
| 131. #486 | D197 | semidirect |
| 139. C4⋊Q8 | C2×D197 | semidirect |
| 155. #102 | C2×D197 | semidirect |
| 158. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #127×D197 | 2 |
| #27161442 | 2 |
| #27161427 | 2 |
| #27161426 | 2 |
| #27161425 | 2 |
| #27161082 | 2 |
| C4×#15691341 | 2 |
| #486×C197 | 2 |
| #3138 | 197 |