Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 1. C2×#20263359 | C2 | semidirect |
| 3. C22×#15691346 | C2 | semidirect |
| 4. C2×#20263334 | C2 | semidirect |
| 5. #27161341 | C2 | direct (N × H) |
| 6. C2×#20263261 | C2 | semidirect |
| 7. C2×#20263244 | C2 | semidirect |
| 8. C2×#100×C197 | C2 | semidirect |
| 12. #20263359 | C22 | semidirect |
| 21. C2×#15691346 | C22 | semidirect |
| 24. #20263334 | C22 | semidirect |
| 29. #20263261 | C22 | semidirect |
| 30. #20263244 | C22 | semidirect |
| 34. #100×C197 | C22 | semidirect |
| 135. C2×C197 | #471 | semidirect |
| 138. C197 | C2×#471 | semidirect |
| 147. C2×#100 | D197 | semidirect |
| 173. #100 | C2×D197 | semidirect |
| 275. C2 | #27161341 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263359 | 2 |
| C2×#20263352 | 2 |
| C22×#15691346 | 2 |
| C2×#20263334 | 2 |
| #27161341 | 2 |
| C2×#20263261 | 2 |
| C2×#20263244 | 2 |
| C2×#100×C197 | 2 |
| C2×#471 | 197 |