Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161879 | C2 | semidirect |
| 2. C2×#20263352 | C2 | semidirect |
| 3. C2×#20263352 | C2 | semidirect |
| 4. #27161845 | C2 | semidirect |
| 5. #27161348 | C2 | semidirect |
| 6. #27161341 | C2 | semidirect |
| 7. #27161127 | C2 | semidirect |
| 8. #27161061 | C2 | semidirect |
| 9. C2×#100×C197 | C2 | semidirect |
| 13. #20263359 | C22 | semidirect |
| 15. #20263354 | C22 | semidirect |
| 22. C2×#15691346 | C22 | semidirect |
| 24. C2×#15691343 | C22 | semidirect |
| 25. #20263334 | C22 | semidirect |
| 30. #20263261 | C22 | semidirect |
| 31. #20263244 | C22 | semidirect |
| 32. #20263242 | C22 | semidirect |
| 36. #100×C197 | C22 | semidirect |
| 147. C197 | #3068 | semidirect |
| 157. C2×#100 | D197 | semidirect |
| 184. #100 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161879 | 2 |
| C2×#20263352 | 2 |
| #27161845 | 2 |
| #27161348 | 2 |
| #27161341 | 2 |
| #27161127 | 2 |
| #27161061 | 2 |
| C2×#100×C197 | 2 |
| #3068 | 197 |