Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #27161877 | C2 | semidirect |
| 2. C2×#20263352 | C2 | semidirect |
| 3. #27161845 | C2 | semidirect |
| 4. #27161346 | C2 | semidirect |
| 5. #27161339 | C2 | semidirect |
| 6. #27161128 | C2 | semidirect |
| 7. #27161063 | C2 | semidirect |
| 8. C2×#20263243 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C197 | C2 | semidirect |
| 11. #20263357 | C22 | semidirect |
| 15. #20263352 | C22 | semidirect |
| 21. #20263332 | C22 | semidirect |
| 26. #20263262 | C22 | semidirect |
| 27. #20263245 | C22 | semidirect |
| 28. #20263243 | C22 | semidirect |
| 29. #20263243 | C22 | semidirect |
| 34. C2×SD16×C197 | C22 | semidirect |
| 35. C2×D8×C197 | C22 | semidirect |
| 147. C197 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D197 | semidirect |
| 171. C2×SD16 | C2×D197 | semidirect |
| 173. C2×D8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| C2×#20263352 | 2 |
| #27161845 | 2 |
| #27161346 | 2 |
| #27161339 | 2 |
| #27161128 | 2 |
| #27161063 | 2 |
| C2×#20263243 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #3068 | 197 |