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×#20263371 | C2 | semidirect |
| 2. C2×#20263354 | C2 | semidirect |
| 3. C22×#15691343 | C2 | semidirect |
| 4. #27161648 | C2 | semidirect |
| 5. #27161225 | C2 | semidirect |
| 6. #27161214 | C2 | semidirect |
| 7. #27161073 | C2 | semidirect |
| 8. #27161047 | C2 | semidirect |
| 9. #418×C197 | C2 | semidirect |
| 15. C2×#15691357 | C22 | semidirect |
| 16. C22×D788 | C22 | semidirect |
| 19. C2×D4×D197 | C22 | semidirect |
| 21. C2×#15691347 | C22 | semidirect |
| 22. C2×D1576 | C22 | semidirect |
| 24. C2×#15691343 | C22 | semidirect |
| 25. C22×#13096802 | C22 | semidirect |
| 28. #20263301 | C22 | semidirect |
| 30. #20263249 | C22 | semidirect |
| 31. #20263246 | C22 | semidirect |
| 32. #20263238 | C22 | semidirect |
| 34. C2×M16×C197 | C22 | semidirect |
| 35. #117×C197 | C22 | semidirect |
| 36. #102×C197 | C22 | semidirect |
| 42. #15691358 | D4 | semidirect |
| 75. C2×D4×C197 | D4 | semidirect |
| 151. C197 | #3008 | semidirect |
| 159. #418 | D197 | semidirect |
| 178. C2×M16 | C2×D197 | semidirect |
| 184. #117 | C2×D197 | semidirect |
| 187. #102 | C2×D197 | semidirect |
| 218. C2×D4 | D788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263371 | 2 |
| C2×#20263354 | 2 |
| C22×#15691343 | 2 |
| #27161648 | 2 |
| #27161225 | 2 |
| #27161214 | 2 |
| #27161073 | 2 |
| #27161047 | 2 |
| #418×C197 | 2 |
| #3008 | 197 |