Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#20263241 | C2 | semidirect |
| 3. #27160871 | C2 | direct (N × H) |
| 4. C2×#99×C197 | C2 | semidirect |
| 5. C22×D788 | C4 | semidirect |
| 10. #20263322 | C4 | semidirect |
| 13. C2×C4×Dic197 | C4 | semidirect |
| 15. #20263241 | C22 | semidirect |
| 19. #99×C197 | C22 | semidirect |
| 24. C2×D788 | C2×C4 | semidirect |
| 36. C4×Dic197 | C2×C4 | semidirect |
| 117. C2×C197 | #353 | semidirect |
| 120. C197 | C2×#353 | semidirect |
| 124. C2×#99 | D197 | semidirect |
| 140. #99 | C2×D197 | semidirect |
| 239. C2 | #27160871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263322 | 2 |
| C2×#20263241 | 2 |
| #27160871 | 2 |
| C2×#99×C197 | 2 |
| C2×#353 | 197 |