Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. M32×D197 | C2 | semidirect |
| 3. C2×C16×D197 | C2 | semidirect |
| 4. #27160864 | C2 | semidirect |
| 5. #27160863 | C2 | semidirect |
| 6. #27160862 | C2 | semidirect |
| 7. #350×C197 | C2 | semidirect |
| 18. #20263266 | C22 | semidirect |
| 20. C2×#15691333 | C22 | semidirect |
| 25. M32×C197 | C22 | semidirect |
| 26. C2×C16×C197 | C22 | semidirect |
| 107. D197 | #350 | direct (N × H) |
| 108. C197 | C2×#350 | semidirect |
| 116. #350 | D197 | direct (N × H) |
| 130. M32 | C2×D197 | semidirect |
| 135. C2×C16 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D197 | 2 |
| M32×D197 | 2 |
| C2×C16×D197 | 2 |
| #27160864 | 2 |
| #27160863 | 2 |
| #27160862 | 2 |
| #350×C197 | 2 |
| C2×#350 | 197 |