Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #27161495 | C2 | semidirect |
| 3. #27160899 | C2 | semidirect |
| 4. #27160864 | C2 | semidirect |
| 5. #27160863 | C2 | semidirect |
| 6. #27160854 | C2 | semidirect |
| 7. #504×C197 | C2 | semidirect |
| 71. C197 | #2171 | semidirect |
| 74. #504 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161495 | 2 |
| #27161194 | 2 |
| #27160899 | 2 |
| #27160864 | 2 |
| #27160863 | 2 |
| #27160854 | 2 |
| #504×C197 | 2 |
| #2171 | 197 |