Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161799 | C2 | semidirect |
| 3. #27161430 | C2 | semidirect |
| 4. #27161421 | C2 | semidirect |
| 5. #27161360 | C2 | semidirect |
| 6. #27161320 | C2 | semidirect |
| 7. #27161290 | C2 | semidirect |
| 8. #27161243 | C2 | semidirect |
| 9. C4×#15691347 | C2 | semidirect |
| 10. #27161076 | C2 | semidirect |
| 11. C8×D4×C197 | C2 | semidirect |
| 125. C197 | #3302 | semidirect |
| 136. C8×D4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161799 | 2 |
| #27161734 | 2 |
| #27161430 | 2 |
| #27161421 | 2 |
| #27161360 | 2 |
| #27161320 | 2 |
| #27161290 | 2 |
| #27161243 | 2 |
| C4×#15691347 | 2 |
| #27161076 | 2 |
| C8×D4×C197 | 2 |
| #3302 | 197 |