Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #27161893 | C2 | semidirect |
| 2. #27161891 | C2 | semidirect |
| 3. #27161881 | C2 | semidirect |
| 4. #27161463 | C2 | semidirect |
| 5. #27161355 | C2 | semidirect |
| 6. #27161350 | C2 | semidirect |
| 7. #27161342 | C2 | semidirect |
| 8. #27161258 | C2 | semidirect |
| 9. #27161253 | C2 | semidirect |
| 10. #27161197 | C2 | semidirect |
| 11. #443×C197 | C2 | semidirect |
| 12. #20263373 | C22 | semidirect |
| 16. #20263356 | C22 | semidirect |
| 19. #20263354 | C22 | semidirect |
| 26. C2×Dic788 | C22 | semidirect |
| 29. C2×#15691347 | C22 | semidirect |
| 33. #20263332 | C22 | semidirect |
| 34. #20263314 | C22 | semidirect |
| 35. #20263262 | C22 | semidirect |
| 37. #20263254 | C22 | semidirect |
| 38. #20263244 | C22 | semidirect |
| 39. #20263242 | C22 | semidirect |
| 41. #131×C197 | C22 | semidirect |
| 42. #108×C197 | C22 | semidirect |
| 43. #104×C197 | C22 | semidirect |
| 44. C4×C8×C197 | C22 | semidirect |
| 149. C197 | #3290 | semidirect |
| 161. #443 | D197 | semidirect |
| 185. #131 | C2×D197 | semidirect |
| 188. #108 | C2×D197 | semidirect |
| 191. #104 | C2×D197 | semidirect |
| 194. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161893 | 2 |
| #27161891 | 2 |
| #27161881 | 2 |
| #27161463 | 2 |
| #27161355 | 2 |
| #27161350 | 2 |
| #27161342 | 2 |
| #27161258 | 2 |
| #27161253 | 2 |
| #27161197 | 2 |
| #443×C197 | 2 |
| #3290 | 197 |