Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#20263284 | C2 | semidirect |
| 3. #27161423 | C2 | semidirect |
| 4. #27161422 | C2 | semidirect |
| 5. #27161406 | C2 | semidirect |
| 6. #27161405 | C2 | semidirect |
| 7. #27161122 | C2 | semidirect |
| 8. #27161081 | C2 | semidirect |
| 9. #27161078 | C2 | semidirect |
| 10. #27161042 | C2 | semidirect |
| 11. #428×C197 | C2 | semidirect |
| 30. #20263259 | C22 | semidirect |
| 31. #20263257 | C22 | semidirect |
| 32. #20263251 | C22 | semidirect |
| 33. #20263249 | C22 | semidirect |
| 34. #20263248 | C22 | semidirect |
| 35. #20263246 | C22 | semidirect |
| 41. #107×C197 | C22 | semidirect |
| 42. #106×C197 | C22 | semidirect |
| 152. C197 | #3093 | semidirect |
| 161. #428 | D197 | semidirect |
| 187. #107 | C2×D197 | semidirect |
| 189. #106 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161591 | 2 |
| C2×#20263284 | 2 |
| #27161423 | 2 |
| #27161422 | 2 |
| #27161406 | 2 |
| #27161405 | 2 |
| #27161122 | 2 |
| #27161081 | 2 |
| #27161078 | 2 |
| #27161042 | 2 |
| #428×C197 | 2 |
| #3093 | 197 |