Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161914 | C2 | semidirect |
| 2. #27161585 | C2 | semidirect |
| 3. #27161270 | C2 | semidirect |
| 4. #27161269 | C2 | semidirect |
| 5. #27161265 | C2 | semidirect |
| 6. #27161051 | C2 | semidirect |
| 7. B(4,𝔽2)×C197 | C2 | semidirect |
| 14. C23×Dic197 | C22 | semidirect |
| 15. #20263310 | C22 | semidirect |
| 16. #20263307 | C22 | semidirect |
| 19. #20263295 | C22 | semidirect |
| 22. #20263282 | C22 | semidirect |
| 23. #20263241 | C22 | semidirect |
| 24. #20263240 | C22 | semidirect |
| 26. #120×C197 | C22 | semidirect |
| 27. #99×C197 | C22 | semidirect |
| 37. C2×Dic394 | D4 | semidirect |
| 42. C2×C22⋊D197 | D4 | semidirect |
| 49. C22×Dic197 | D4 | semidirect |
| 53. C2×C4×D197 | D4 | semidirect |
| 126. C197 | #3025 | semidirect |
| 133. B(4,𝔽2) | D197 | semidirect |
| 148. #120 | C2×D197 | semidirect |
| 154. #99 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161914 | 2 |
| #27161585 | 2 |
| #27161270 | 2 |
| #27161269 | 2 |
| #27161265 | 2 |
| #27161051 | 2 |
| B(4,𝔽2)×C197 | 2 |
| #3025 | 197 |