Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#20263352 | C2 | semidirect |
| 2. #27161629 | C2 | semidirect |
| 3. #27161294 | C2 | semidirect |
| 4. #27161284 | C2 | semidirect |
| 5. #27161274 | C2 | semidirect |
| 6. #27161103 | C2 | semidirect |
| 7. #27161078 | C2 | semidirect |
| 8. C2×C4×D4×C197 | C2 | semidirect |
| 14. #20263326 | C22 | semidirect |
| 15. #20263323 | C22 | semidirect |
| 16. #20263314 | C22 | semidirect |
| 21. C4⋊#13096802 | C22 | semidirect |
| 22. C4⋊#13096802 | C22 | semidirect |
| 23. #20263249 | C22 | semidirect |
| 24. #20263246 | C22 | semidirect |
| 53. C2×D4×C197 | D4 | semidirect |
| 119. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 129. C197 | #3036 | semidirect |
| 133. C2×C4×D4 | D197 | semidirect |
| 174. C2×D4 | D788 | semidirect |
| 250. C4 | #20263352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| #27161629 | 2 |
| #27161294 | 2 |
| #27161284 | 2 |
| #27161274 | 2 |
| #27161103 | 2 |
| #27161078 | 2 |
| C2×C4×D4×C197 | 2 |
| #3036 | 197 |