Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#20263291 | C2 | semidirect |
| 4. #27160985 | C2 | semidirect |
| 5. #27160973 | C2 | semidirect |
| 6. #27160951 | C2 | semidirect |
| 7. #27160948 | C2 | semidirect |
| 8. #27160925 | C2 | semidirect |
| 12. #20263313 | C4 | semidirect |
| 32. C2×Dic394 | C2×C4 | semidirect |
| 44. C22⋊Dic197 | C2×C4 | semidirect |
| 46. C4×Dic197 | C2×C4 | semidirect |
| 111. C197 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263313 | 2 |
| C2×#20263291 | 2 |
| C2×D4×Dic197 | 2 |
| #27160985 | 2 |
| #27160973 | 2 |
| #27160951 | 2 |
| #27160948 | 2 |
| #27160925 | 2 |
| #390×C197 | 2 |
| #2326 | 197 |