Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161653 | C2 | semidirect |
| 3. #27161268 | C2 | semidirect |
| 4. #27161053 | C2 | semidirect |
| 5. #27161052 | C2 | semidirect |
| 6. #536×C197 | C2 | semidirect |
| 17. #20263309 | C22 | semidirect |
| 19. #20263285 | C22 | semidirect |
| 20. #20263241 | C22 | semidirect |
| 21. #20263240 | C22 | semidirect |
| 23. C22×Q8×C197 | C22 | semidirect |
| 26. #123×C197 | C22 | semidirect |
| 28. #117×C197 | C22 | semidirect |
| 128. C197 | #3028 | semidirect |
| 132. #536 | D197 | semidirect |
| 145. C22×Q8 | C2×D197 | semidirect |
| 151. #123 | C2×D197 | semidirect |
| 155. #117 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161915 | 2 |
| #27161653 | 2 |
| #27161268 | 2 |
| #27161053 | 2 |
| #27161052 | 2 |
| #536×C197 | 2 |
| #3028 | 197 |