Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20263357 | C2 | semidirect |
| 3. #27161653 | C2 | semidirect |
| 4. #27161238 | C2 | semidirect |
| 5. #27161228 | C2 | semidirect |
| 6. #27161084 | C2 | semidirect |
| 7. #27161076 | C2 | semidirect |
| 8. #27161045 | C2 | semidirect |
| 9. C22×SD16×C197 | C2 | semidirect |
| 20. C2×#15691348 | C22 | semidirect |
| 21. C2×#15691345 | C22 | semidirect |
| 22. C2×#15691342 | C22 | semidirect |
| 26. #20263302 | C22 | semidirect |
| 27. #20263285 | C22 | semidirect |
| 28. #20263251 | C22 | semidirect |
| 29. #20263248 | C22 | semidirect |
| 30. #20263247 | C22 | semidirect |
| 31. #20263238 | C22 | semidirect |
| 32. C22×Q8×C197 | C22 | semidirect |
| 35. C2×SD16×C197 | C22 | semidirect |
| 36. C22×C8×C197 | C22 | semidirect |
| 146. C197 | #3009 | semidirect |
| 150. C22×SD16 | D197 | semidirect |
| 163. C22×Q8 | C2×D197 | semidirect |
| 172. C2×SD16 | C2×D197 | semidirect |
| 174. C22×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263371 | 2 |
| C2×#20263357 | 2 |
| #27161653 | 2 |
| #27161238 | 2 |
| #27161228 | 2 |
| #27161084 | 2 |
| #27161076 | 2 |
| #27161045 | 2 |
| C22×SD16×C197 | 2 |
| #3009 | 197 |