Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#20263373 | C2 | semidirect |
| 2. #27161877 | C2 | semidirect |
| 3. #27161650 | C2 | semidirect |
| 4. #27161260 | C2 | semidirect |
| 5. #27161250 | C2 | semidirect |
| 6. #27161096 | C2 | semidirect |
| 7. #27161095 | C2 | semidirect |
| 8. C2×#20263244 | C2 | semidirect |
| 9. #575×C197 | C2 | semidirect |
| 21. #20263357 | C22 | semidirect |
| 23. #20263352 | C22 | semidirect |
| 27. #20263324 | C22 | semidirect |
| 28. #20263313 | C22 | semidirect |
| 32. #20263253 | C22 | semidirect |
| 33. #20263252 | C22 | semidirect |
| 34. #20263244 | C22 | semidirect |
| 38. #137×C197 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C197 | C22 | semidirect |
| 185. C197 | #3020 | semidirect |
| 189. #575 | D197 | semidirect |
| 212. #137 | C2×D197 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263373 | 2 |
| #27161877 | 2 |
| #27161650 | 2 |
| #27161260 | 2 |
| #27161250 | 2 |
| #27161096 | 2 |
| #27161095 | 2 |
| C2×#20263244 | 2 |
| #575×C197 | 2 |
| #3020 | 197 |