Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #27161445 | C2 | semidirect |
| 3. #27161441 | C2 | semidirect |
| 4. #27161436 | C2 | semidirect |
| 5. #27161427 | C2 | semidirect |
| 6. #27161083 | C2 | semidirect |
| 7. #27161078 | C2 | semidirect |
| 8. #27161073 | C2 | semidirect |
| 9. C2×#20263246 | C2 | semidirect |
| 10. #27161035 | C2 | semidirect |
| 11. #544×C197 | C2 | semidirect |
| 21. #20263249 | C22 | semidirect |
| 22. #20263249 | C22 | semidirect |
| 23. #20263249 | C22 | semidirect |
| 28. #20263246 | C22 | semidirect |
| 29. #20263246 | C22 | semidirect |
| 30. #20263246 | C22 | semidirect |
| 31. #20263237 | C22 | semidirect |
| 32. C4×#13096802 | C22 | semidirect |
| 34. C4⋊Q8×C197 | C22 | semidirect |
| 36. #125×C197 | C22 | semidirect |
| 135. C197 | #3136 | semidirect |
| 137. #544 | D197 | semidirect |
| 153. C4⋊Q8 | C2×D197 | semidirect |
| 156. #125 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161648 | 2 |
| #27161445 | 2 |
| #27161441 | 2 |
| #27161436 | 2 |
| #27161427 | 2 |
| #27161083 | 2 |
| #27161078 | 2 |
| #27161073 | 2 |
| C2×#20263246 | 2 |
| #27161035 | 2 |
| #544×C197 | 2 |
| #3136 | 197 |