Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 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 |
|---|---|---|
| 3. #27160952 | C2 | semidirect |
| 4. #27160951 | C2 | semidirect |
| 5. #27160937 | C2 | semidirect |
| 9. C2×#15691337 | C22 | semidirect |
| 11. C2×C22⋊Dic197 | C4 | semidirect |
| 16. #20263233 | C22 | semidirect |
| 25. C22×Dic197 | C2×C4 | semidirect |
| 31. C22⋊Dic197 | C2×C4 | semidirect |
| 32. C22⋊Dic197 | C2×C4 | semidirect |
| 57. C23×C197 | C4⋊C4 | semidirect |
| 98. C197 | #2315 | semidirect |
| 150. C23 | #15691337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic197 | 2 |
| #27160952 | 2 |
| #27160951 | 2 |
| #27160937 | 2 |
| C22×C22⋊C4×C197 | 2 |
| #2315 | 197 |