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. #27160984 | C2 | semidirect |
| 6. #27160969 | C2 | semidirect |
| 7. #27160950 | C2 | semidirect |
| 8. #27160925 | C2 | semidirect |
| 9. #384×C197 | C2 | semidirect |
| 13. #20263314 | C4 | semidirect |
| 33. C2×Dic394 | C2×C4 | semidirect |
| 46. #15691335 | C2×C4 | semidirect |
| 57. C42×C197 | C2×C4 | semidirect |
| 111. C197 | #2326 | semidirect |
| 120. #384 | D197 | semidirect |
| 169. C42 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263314 | 2 |
| C2×#20263291 | 2 |
| C2×#20263288 | 2 |
| #27160984 | 2 |
| #27160980 | 2 |
| #27160969 | 2 |
| #27160950 | 2 |
| #27160925 | 2 |
| #384×C197 | 2 |
| #2326 | 197 |