Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27161192 | C2 | semidirect |
| 3. #27160903 | C2 | semidirect |
| 4. #27160891 | C2 | semidirect |
| 5. #27160889 | C2 | semidirect |
| 6. #27160857 | C2 | semidirect |
| 7. #444×C197 | C2 | semidirect |
| 10. #20263269 | C4 | semidirect |
| 11. #20263267 | C4 | semidirect |
| 28. #15691333 | C2×C4 | semidirect |
| 30. Q16×C197 | C2×C4 | semidirect |
| 32. D8×C197 | C2×C4 | semidirect |
| 68. C197 | AGL(1,ℤ/16) | semidirect |
| 71. #444 | 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 |
| #27161192 | 2 |
| #27160903 | 2 |
| #27160891 | 2 |
| #27160889 | 2 |
| #27160857 | 2 |
| #444×C197 | 2 |
| AGL(1,ℤ/16) | 197 |