Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 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. C2×#20263269 | C2 | semidirect |
| 3. #27161317 | C2 | semidirect |
| 4. #27160881 | C2 | semidirect |
| 5. #27160880 | C2 | semidirect |
| 6. #27160858 | C2 | semidirect |
| 7. C2×SD32×C197 | C2 | semidirect |
| 16. C2×#15691333 | C22 | semidirect |
| 17. #20263260 | C22 | semidirect |
| 19. C2×Q16×C197 | C22 | semidirect |
| 22. C2×C16×C197 | C22 | semidirect |
| 79. C2×D197 | SD32 | semidirect |
| 91. C197 | #2187 | semidirect |
| 95. C2×SD32 | D197 | semidirect |
| 101. C2×Q16 | C2×D197 | semidirect |
| 112. C2×C16 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D197 | 2 |
| C2×#20263269 | 2 |
| #27161317 | 2 |
| #27160881 | 2 |
| #27160880 | 2 |
| #27160858 | 2 |
| C2×SD32×C197 | 2 |
| #2187 | 197 |