Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #27161636 | C2 | semidirect |
| 3. #27161421 | C2 | semidirect |
| 4. #27161375 | C2 | semidirect |
| 5. #27161370 | C2 | semidirect |
| 6. #27161290 | C2 | semidirect |
| 7. #27161285 | C2 | semidirect |
| 9. #27161187 | C2 | semidirect |
| 10. #27161181 | C2 | semidirect |
| 11. #432×C197 | C2 | semidirect |
| 136. C197 | #3116 | semidirect |
| 148. #432 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| C4×#15691358 | 2 |
| #27161421 | 2 |
| #27161375 | 2 |
| #27161370 | 2 |
| #27161290 | 2 |
| #27161285 | 2 |
| #27161243 | 2 |
| #27161187 | 2 |
| #27161181 | 2 |
| #432×C197 | 2 |
| #3116 | 197 |