Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 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 |
|---|---|---|
| 1. C2×#20263372 | C2 | semidirect |
| 2. C2×#20263351 | C2 | semidirect |
| 3. C22×D1576 | C2 | semidirect |
| 4. #27161648 | C2 | semidirect |
| 5. #27161227 | C2 | semidirect |
| 6. #27161214 | C2 | semidirect |
| 7. #27161083 | C2 | semidirect |
| 8. #27161045 | C2 | semidirect |
| 9. #416×C197 | C2 | semidirect |
| 12. C2×#15691359 | C22 | semidirect |
| 17. C22×D788 | C22 | semidirect |
| 19. C2×D4×D197 | C22 | semidirect |
| 21. C2×#15691345 | C22 | semidirect |
| 23. C2×D1576 | C22 | semidirect |
| 24. C2×#15691343 | C22 | semidirect |
| 25. C2×#15691342 | C22 | semidirect |
| 28. #20263301 | C22 | semidirect |
| 30. #20263246 | C22 | semidirect |
| 31. #20263238 | C22 | semidirect |
| 33. C22×C8×C197 | C22 | semidirect |
| 34. #117×C197 | C22 | semidirect |
| 35. #103×C197 | C22 | semidirect |
| 36. #102×C197 | C22 | semidirect |
| 55. C2×D788 | D4 | semidirect |
| 72. #41×C197 | D4 | semidirect |
| 151. C197 | #3008 | semidirect |
| 160. #416 | D197 | semidirect |
| 179. C22×C8 | C2×D197 | semidirect |
| 184. #117 | C2×D197 | semidirect |
| 185. #103 | C2×D197 | semidirect |
| 187. #102 | C2×D197 | semidirect |
| 198. #41 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263372 | 2 |
| C2×#20263351 | 2 |
| C22×D1576 | 2 |
| #27161648 | 2 |
| #27161227 | 2 |
| #27161214 | 2 |
| #27161083 | 2 |
| #27161045 | 2 |
| #416×C197 | 2 |
| #3008 | 197 |