Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 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. C4⋊Q8×D197 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161426 | C2 | semidirect |
| 5. #27161425 | C2 | semidirect |
| 6. #27161424 | C2 | semidirect |
| 7. #102×D197 | C2 | semidirect |
| 8. C4×C8×D197 | C2 | semidirect |
| 9. #486×C197 | C2 | semidirect |
| 15. #20263326 | C22 | semidirect |
| 17. #20263325 | C22 | semidirect |
| 26. #20263248 | C22 | semidirect |
| 27. #20263247 | C22 | semidirect |
| 28. #20263246 | C22 | semidirect |
| 29. C4×#13096802 | C22 | semidirect |
| 30. C8×Dic197 | C22 | semidirect |
| 31. C4⋊Q8×C197 | C22 | semidirect |
| 33. #102×C197 | C22 | semidirect |
| 34. C4×C8×C197 | C22 | semidirect |
| 125. D197 | #486 | direct (N × H) |
| 126. C197 | C2×#486 | semidirect |
| 134. #486 | D197 | direct (N × H) |
| 146. C4⋊Q8 | C2×D197 | semidirect |
| 158. #102 | C2×D197 | semidirect |
| 161. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D197 | 2 |
| #127×D197 | 2 |
| #27161427 | 2 |
| #27161426 | 2 |
| #27161425 | 2 |
| #27161424 | 2 |
| #102×D197 | 2 |
| C4×C8×D197 | 2 |
| #486×C197 | 2 |
| C2×#486 | 197 |