Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#20263354 | C2 | semidirect |
| 2. C2×#20263348 | C2 | semidirect |
| 3. #27161648 | C2 | semidirect |
| 4. #27161559 | C2 | semidirect |
| 5. #27161302 | C2 | semidirect |
| 6. #27161295 | C2 | semidirect |
| 7. #27161280 | C2 | semidirect |
| 8. #27161275 | C2 | semidirect |
| 9. #27161081 | C2 | semidirect |
| 10. C2×#20263248 | C2 | semidirect |
| 11. #424×C197 | C2 | semidirect |
| 17. C2×Dic788 | C22 | semidirect |
| 19. C2×#15691347 | C22 | semidirect |
| 20. C2×#15691347 | C22 | semidirect |
| 22. C2×D1576 | C22 | semidirect |
| 28. C4×Dic394 | C22 | semidirect |
| 29. C4×D788 | C22 | semidirect |
| 34. #20263251 | C22 | semidirect |
| 37. #20263248 | C22 | semidirect |
| 41. C4⋊C8×C197 | C22 | semidirect |
| 42. C4⋊C8×C197 | C22 | semidirect |
| 47. #15691358 | D4 | semidirect |
| 154. C197 | #3045 | semidirect |
| 164. #424 | D197 | semidirect |
| 192. C4⋊C8 | C2×D197 | semidirect |
| 193. 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 |
| C2×#20263348 | 2 |
| #27161648 | 2 |
| #27161559 | 2 |
| #27161302 | 2 |
| #27161295 | 2 |
| #27161280 | 2 |
| #27161275 | 2 |
| #27161081 | 2 |
| C2×#20263248 | 2 |
| #424×C197 | 2 |
| #3045 | 197 |