Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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×#20263351 | C2 | semidirect |
| 2. C2×C4×D788 | C2 | semidirect |
| 3. #27161291 | C2 | semidirect |
| 4. #27161281 | C2 | semidirect |
| 5. #27161271 | C2 | semidirect |
| 6. #27161103 | C2 | semidirect |
| 7. #27161080 | C2 | semidirect |
| 8. #532×C197 | C2 | semidirect |
| 21. C4⋊#13096802 | C22 | semidirect |
| 22. C4⋊#13096802 | C22 | semidirect |
| 23. #20263250 | C22 | semidirect |
| 24. #20263247 | C22 | semidirect |
| 26. C4⋊Q8×C197 | C22 | semidirect |
| 27. #127×C197 | C22 | semidirect |
| 28. #124×C197 | C22 | semidirect |
| 37. C2×D788 | D4 | semidirect |
| 119. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 129. C197 | #3036 | semidirect |
| 132. #532 | D197 | semidirect |
| 146. C4⋊Q8 | C2×D197 | semidirect |
| 147. #127 | C2×D197 | semidirect |
| 148. #124 | C2×D197 | semidirect |
| 250. C4 | #20263351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C2×C4×D788 | 2 |
| #27161291 | 2 |
| #27161281 | 2 |
| #27161271 | 2 |
| #27161103 | 2 |
| #27161080 | 2 |
| #532×C197 | 2 |
| #3036 | 197 |