Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #27160960 | C2 | semidirect |
| 4. #27160945 | C2 | semidirect |
| 6. C4⋊C4×Dic197 | C2 | semidirect |
| 7. #384×C197 | C2 | semidirect |
| 9. #20263283 | C4 | semidirect |
| 88. C197 | #2314 | semidirect |
| 93. #384 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263283 | 2 |
| #27160969 | 2 |
| #27160960 | 2 |
| #27160945 | 2 |
| #27160936 | 2 |
| C4⋊C4×Dic197 | 2 |
| #384×C197 | 2 |
| #2314 | 197 |