Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
278 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #27160869 | C2 | direct (N × H) |
| 12. C23×C4×C197 | C4 | semidirect |
| 15. #123×C197 | C4 | semidirect |
| 19. C2×C22⋊C4×C197 | C4 | semidirect |
| 39. C22×C4×C197 | C2×C4 | semidirect |
| 46. C22⋊C4×C197 | C2×C4 | semidirect |
| 103. C2×C197 | #352 | semidirect |
| 105. C197 | C2×#352 | semidirect |
| 112. C23×C4 | Dic197 | semidirect |
| 116. #123 | Dic197 | semidirect |
| 121. C2×C22⋊C4 | Dic197 | semidirect |
| 140. C22×C4 | C2×Dic197 | semidirect |
| 152. C22⋊C4 | C2×Dic197 | semidirect |
| 209. C2 | #27160869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263243 | 2 |
| C2×#20263241 | 2 |
| #27160869 | 2 |
| C2×#123×C197 | 2 |
| C2×#352 | 197 |