Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #27160906 | C2 | semidirect |
| 3. #27160904 | C2 | semidirect |
| 4. #27160879 | C2 | semidirect |
| 5. #27160879 | C2 | semidirect |
| 6. C22⋊#15691333 | C2 | semidirect |
| 7. #427×C197 | C2 | semidirect |
| 69. C197 | #2234 | semidirect |
| 72. #427 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161315 | 2 |
| #27160906 | 2 |
| #27160904 | 2 |
| #27160879 | 2 |
| C22⋊#15691333 | 2 |
| #427×C197 | 2 |
| #2234 | 197 |