Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161896 | C2 | semidirect |
| 2. #27161889 | C2 | semidirect |
| 3. #27161880 | C2 | semidirect |
| 4. #27161462 | C2 | semidirect |
| 5. #27161355 | C2 | semidirect |
| 6. #27161341 | C2 | semidirect |
| 7. #27161259 | C2 | semidirect |
| 8. #27161250 | C2 | semidirect |
| 9. #27161195 | C2 | semidirect |
| 10. #27161194 | C2 | semidirect |
| 11. #472×C197 | C2 | semidirect |
| 12. #20263373 | C22 | semidirect |
| 16. #20263359 | C22 | semidirect |
| 27. C2×Dic788 | C22 | semidirect |
| 28. C2×#15691346 | C22 | semidirect |
| 31. #20263334 | C22 | semidirect |
| 33. #20263313 | C22 | semidirect |
| 34. #20263261 | C22 | semidirect |
| 35. #20263253 | C22 | semidirect |
| 37. #20263252 | C22 | semidirect |
| 38. #20263244 | C22 | semidirect |
| 39. C8×Dic197 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C197 | C22 | semidirect |
| 42. #131×C197 | C22 | semidirect |
| 43. #108×C197 | C22 | semidirect |
| 44. #100×C197 | C22 | semidirect |
| 149. C197 | #3290 | semidirect |
| 156. #472 | D197 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D197 | semidirect |
| 185. #131 | C2×D197 | semidirect |
| 188. #108 | C2×D197 | semidirect |
| 193. #100 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161896 | 2 |
| #27161889 | 2 |
| #27161880 | 2 |
| #27161462 | 2 |
| #27161355 | 2 |
| #27161341 | 2 |
| #27161259 | 2 |
| #27161250 | 2 |
| #27161195 | 2 |
| #27161194 | 2 |
| #472×C197 | 2 |
| #3290 | 197 |