Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #27161794 | C2 | semidirect |
| 2. #27161425 | C2 | semidirect |
| 3. #27161400 | C2 | semidirect |
| 4. #27161374 | C2 | semidirect |
| 5. #27161313 | C2 | semidirect |
| 6. #27161271 | C2 | semidirect |
| 7. #27161224 | C2 | semidirect |
| 8. C4×#15691345 | C2 | semidirect |
| 9. D4×#13096802 | C2 | semidirect |
| 10. #27161075 | C2 | semidirect |
| 11. #550×C197 | C2 | semidirect |
| 132. C197 | #3305 | semidirect |
| 135. #550 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161794 | 2 |
| #27161425 | 2 |
| #27161400 | 2 |
| #27161374 | 2 |
| #27161313 | 2 |
| #27161271 | 2 |
| #27161224 | 2 |
| C4×#15691345 | 2 |
| D4×#13096802 | 2 |
| #27161075 | 2 |
| #550×C197 | 2 |
| #3305 | 197 |