Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27161053 | C2 | semidirect |
| 3. #27160871 | C2 | semidirect |
| 4. #410×C197 | C2 | semidirect |
| 5. C22×D788 | C4 | semidirect |
| 7. #20263315 | C4 | semidirect |
| 13. #20263285 | C4 | semidirect |
| 15. #20263241 | C22 | semidirect |
| 19. #99×C197 | C22 | semidirect |
| 100. C197 | #2128 | semidirect |
| 104. #410 | D197 | semidirect |
| 120. #99 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161643 | 2 |
| #27161053 | 2 |
| #27160871 | 2 |
| #410×C197 | 2 |
| #2128 | 197 |