Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
688 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 169 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×#20263309 | C2 | semidirect |
| 3. C22×C4×Dic197 | C2 | semidirect |
| 4. #27160979 | C2 | semidirect |
| 5. #27160974 | C2 | semidirect |
| 6. #27160973 | C2 | semidirect |
| 7. #27160969 | C2 | semidirect |
| 8. #27160959 | C2 | semidirect |
| 9. #27160956 | C2 | semidirect |
| 10. #27160937 | C2 | semidirect |
| 11. C2×#123×C197 | C2 | semidirect |
| 72. C22×C4×C197 | D4 | semidirect |
| 150. Dic197 | #123 | semidirect |
| 159. C197 | #2854 | semidirect |
| 162. C2×#123 | D197 | semidirect |
| 221. C22×C4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263309 | 2 |
| C2×#20263298 | 2 |
| C22×C4×Dic197 | 2 |
| #27160979 | 2 |
| #27160974 | 2 |
| #27160973 | 2 |
| #27160969 | 2 |
| #27160959 | 2 |
| #27160956 | 2 |
| #27160937 | 2 |
| C2×#123×C197 | 2 |
| #2854 | 197 |