Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161420 | C2 | semidirect |
| 3. #27161414 | C2 | semidirect |
| 4. #27161403 | C2 | semidirect |
| 5. #27161392 | C2 | semidirect |
| 6. #27161122 | C2 | semidirect |
| 7. C2×#20263259 | C2 | semidirect |
| 8. #27161078 | C2 | semidirect |
| 9. #27161073 | C2 | semidirect |
| 10. #27161046 | C2 | semidirect |
| 11. #520×C197 | C2 | semidirect |
| 133. C197 | #3098 | semidirect |
| 136. #520 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161657 | 2 |
| #27161420 | 2 |
| #27161414 | 2 |
| #27161403 | 2 |
| #27161392 | 2 |
| #27161122 | 2 |
| C2×#20263259 | 2 |
| #27161078 | 2 |
| #27161073 | 2 |
| #27161046 | 2 |
| #520×C197 | 2 |
| #3098 | 197 |