Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #27160979 | C2 | semidirect |
| 3. #27160968 | C2 | semidirect |
| 4. #27160964 | C2 | semidirect |
| 5. #27160957 | C2 | semidirect |
| 6. #27160955 | C2 | semidirect |
| 7. C4×C22⋊Dic197 | C2 | semidirect |
| 8. #27160926 | C2 | semidirect |
| 9. #381×C197 | C2 | semidirect |
| 13. #20263300 | C4 | semidirect |
| 38. C2×C22⋊D197 | C2×C4 | semidirect |
| 45. C4⋊Dic197 | C2×C4 | semidirect |
| 51. #15691335 | C2×C4 | semidirect |
| 58. C22×C4×C197 | C2×C4 | semidirect |
| 134. C197 | #2333 | semidirect |
| 142. #381 | D197 | semidirect |
| 183. C22×C4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263300 | 2 |
| #27160979 | 2 |
| #27160968 | 2 |
| #27160964 | 2 |
| #27160957 | 2 |
| #27160955 | 2 |
| C4×C22⋊Dic197 | 2 |
| #27160926 | 2 |
| #381×C197 | 2 |
| #2333 | 197 |