Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #27161420 | C2 | semidirect |
| 3. #27161414 | C2 | semidirect |
| 4. #27161409 | C2 | semidirect |
| 5. #27161403 | C2 | semidirect |
| 6. #27161397 | C2 | semidirect |
| 7. #27161392 | C2 | semidirect |
| 8. #27161115 | C2 | semidirect |
| 9. #27161073 | C2 | semidirect |
| 10. C2×C22⋊#13096802 | C2 | semidirect |
| 11. C2×#117×C197 | C2 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263259 | C22 | semidirect |
| 25. #20263257 | C22 | semidirect |
| 26. #20263257 | C22 | semidirect |
| 27. #20263249 | C22 | semidirect |
| 28. #20263249 | C22 | semidirect |
| 29. #20263246 | C22 | semidirect |
| 30. #20263246 | C22 | semidirect |
| 143. C197 | #3091 | semidirect |
| 146. C2×#117 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161590 | 2 |
| #27161420 | 2 |
| #27161414 | 2 |
| #27161409 | 2 |
| #27161403 | 2 |
| #27161397 | 2 |
| #27161392 | 2 |
| #27161115 | 2 |
| #27161073 | 2 |
| C2×C22⋊#13096802 | 2 |
| C2×#117×C197 | 2 |
| #3091 | 197 |