Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27161095 | C2 | semidirect |
| 3. #27161075 | C2 | semidirect |
| 4. #27161047 | C2 | semidirect |
| 5. #27160850 | C2 | semidirect |
| 6. #27160843 | C2 | semidirect |
| 7. #568×C197 | C2 | semidirect |
| 10. #20263356 | C4 | semidirect |
| 12. #20263351 | C4 | semidirect |
| 118. C197 | #1881 | semidirect |
| 121. #568 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| #27161095 | 2 |
| #27161075 | 2 |
| #27161047 | 2 |
| #27160850 | 2 |
| #27160843 | 2 |
| #568×C197 | 2 |
| #1881 | 197 |