Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #27161477 | C2 | semidirect |
| 4. #27161418 | C2 | semidirect |
| 5. #27161408 | C2 | semidirect |
| 6. #27161374 | C2 | semidirect |
| 7. #27161364 | C2 | semidirect |
| 8. #27161334 | C2 | semidirect |
| 10. #27161120 | C2 | semidirect |
| 11. C4×Q16×C197 | C2 | semidirect |
| 116. C197 | #3356 | semidirect |
| 126. C4×Q16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161802 | 2 |
| #27161789 | 2 |
| #27161477 | 2 |
| #27161418 | 2 |
| #27161408 | 2 |
| #27161374 | 2 |
| #27161364 | 2 |
| #27161334 | 2 |
| #27161158 | 2 |
| #27161120 | 2 |
| C4×Q16×C197 | 2 |
| #3356 | 197 |