Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
774 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 255 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×#20263333 | C2 | semidirect |
| 3. #27161047 | C2 | semidirect |
| 4. #27161045 | C2 | semidirect |
| 5. #27161042 | C2 | semidirect |
| 6. C2×#20263238 | C2 | semidirect |
| 7. C2×#131×C197 | C2 | semidirect |
| 17. C2×#15691342 | C22 | semidirect |
| 18. C22×#13096802 | C22 | semidirect |
| 21. #20263238 | C22 | semidirect |
| 22. #20263238 | C22 | semidirect |
| 23. #20263238 | C22 | semidirect |
| 26. C2×M16×C197 | C22 | semidirect |
| 27. C22×C8×C197 | C22 | semidirect |
| 96. C2×D197 | #131 | semidirect |
| 108. C197 | #2880 | semidirect |
| 112. C2×#131 | D197 | semidirect |
| 129. C2×M16 | C2×D197 | semidirect |
| 131. 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×#41×D197 | 2 |
| C2×#20263333 | 2 |
| #27161047 | 2 |
| #27161045 | 2 |
| #27161042 | 2 |
| C2×#20263238 | 2 |
| C2×#131×C197 | 2 |
| #2880 | 197 |