Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161629 | C2 | semidirect |
| 2. C4×#15691358 | C2 | semidirect |
| 3. #27161404 | C2 | semidirect |
| 4. #27161365 | C2 | semidirect |
| 5. #27161360 | C2 | semidirect |
| 6. #27161280 | C2 | semidirect |
| 7. #27161275 | C2 | semidirect |
| 8. #27161226 | C2 | semidirect |
| 9. #27161192 | C2 | semidirect |
| 10. #27161181 | C2 | semidirect |
| 11. #432×C197 | C2 | semidirect |
| 87. Dic394 | #41 | semidirect |
| 93. D788 | #41 | semidirect |
| 144. C197 | #3115 | semidirect |
| 156. #432 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161629 | 2 |
| C4×#15691358 | 2 |
| #27161404 | 2 |
| #27161365 | 2 |
| #27161360 | 2 |
| #27161280 | 2 |
| #27161275 | 2 |
| #27161226 | 2 |
| #27161192 | 2 |
| #27161181 | 2 |
| #432×C197 | 2 |
| #3115 | 197 |