Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27160976 | C2 | semidirect |
| 4. #27160973 | C2 | semidirect |
| 5. #27160967 | C2 | semidirect |
| 6. #27160961 | C2 | semidirect |
| 7. #27160952 | C2 | semidirect |
| 8. #27160937 | C2 | semidirect |
| 11. #20263307 | C4 | semidirect |
| 34. C22×Dic197 | C2×C4 | semidirect |
| 43. #15691337 | C2×C4 | semidirect |
| 47. C22⋊Dic197 | C2×C4 | semidirect |
| 126. C197 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263307 | 2 |
| #27160982 | 2 |
| #27160976 | 2 |
| #27160973 | 2 |
| #27160967 | 2 |
| #27160961 | 2 |
| #27160952 | 2 |
| #27160937 | 2 |
| #386×C197 | 2 |
| #2376 | 197 |