Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #27161201 | C2 | semidirect |
| 3. #27161190 | C2 | semidirect |
| 4. #27160901 | C2 | semidirect |
| 5. #27160893 | C2 | semidirect |
| 6. #27160856 | C2 | semidirect |
| 7. #360×C197 | C2 | semidirect |
| 11. #20263269 | C4 | semidirect |
| 12. #20263267 | C4 | semidirect |
| 31. #15691333 | C2×C4 | semidirect |
| 33. Q16×C197 | C2×C4 | semidirect |
| 35. D8×C197 | C2×C4 | semidirect |
| 68. C197 | AGL(1,ℤ/16) | semidirect |
| 75. #360 | D197 | semidirect |
| 93. Q16 | C4×D197 | semidirect |
| 97. D8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161514 | 2 |
| #27161201 | 2 |
| #27161190 | 2 |
| #27160901 | 2 |
| #27160893 | 2 |
| #27160856 | 2 |
| #360×C197 | 2 |
| AGL(1,ℤ/16) | 197 |