Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 1. C2×#20263356 | C2 | semidirect |
| 3. C22×#15691347 | C2 | semidirect |
| 4. #27161342 | C2 | direct (N × H) |
| 5. C2×#20263262 | C2 | semidirect |
| 6. C2×#20263244 | C2 | semidirect |
| 7. C2×#20263242 | C2 | semidirect |
| 8. C2×#131×C197 | C2 | semidirect |
| 12. #20263356 | C22 | semidirect |
| 19. C2×#15691347 | C22 | semidirect |
| 25. #20263262 | C22 | semidirect |
| 26. #20263244 | C22 | semidirect |
| 27. #20263242 | C22 | semidirect |
| 30. #131×C197 | C22 | semidirect |
| 135. C2×C197 | #471 | semidirect |
| 138. C197 | C2×#471 | semidirect |
| 143. C2×#131 | D197 | semidirect |
| 164. #131 | C2×D197 | semidirect |
| 275. C2 | #27161342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C2×#20263351 | 2 |
| C22×#15691347 | 2 |
| #27161342 | 2 |
| C2×#20263262 | 2 |
| C2×#20263244 | 2 |
| C2×#20263242 | 2 |
| C2×#131×C197 | 2 |
| C2×#471 | 197 |