Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C23×#13096802 | C2 | semidirect |
| 3. #27161047 | C2 | direct (N × H) |
| 4. C2×#20263238 | C2 | semidirect |
| 5. C22×M16×C197 | C2 | semidirect |
| 16. C22×#13096802 | C22 | semidirect |
| 17. #20263238 | C22 | semidirect |
| 20. C2×M16×C197 | C22 | semidirect |
| 91. C2×C197 | #408 | semidirect |
| 95. C197 | C2×#408 | semidirect |
| 98. C22×M16 | D197 | semidirect |
| 112. C2×M16 | C2×D197 | semidirect |
| 188. C2 | #27161047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C23×#13096802 | 2 |
| #27161047 | 2 |
| C2×#20263238 | 2 |
| C22×M16×C197 | 2 |
| C2×#408 | 197 |