Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 1. C2×#20263243 | C2 | semidirect |
| 2. C2×#20263241 | C2 | semidirect |
| 3. #27160866 | C2 | direct (N × H) |
| 8. #20263243 | C22 | semidirect |
| 10. #20263241 | C22 | semidirect |
| 11. C25×C197 | C4 | semidirect |
| 16. #120×C197 | C4 | semidirect |
| 19. C2×C22⋊C4×C197 | C4 | semidirect |
| 32. C24×C197 | C2×C4 | semidirect |
| 48. C22⋊C4×C197 | C2×C4 | semidirect |
| 122. C2×C197 | AΣL(1,𝔽16) | semidirect |
| 124. C197 | C2×AΣL(1,𝔽16) | semidirect |
| 130. C25 | Dic197 | semidirect |
| 136. #120 | Dic197 | semidirect |
| 140. C2×C22⋊C4 | Dic197 | semidirect |
| 151. C24 | C2×Dic197 | semidirect |
| 173. C22⋊C4 | C2×Dic197 | semidirect |
| 247. C2 | #27160866 | 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 |
| #27160866 | 2 |
| C2×#120×C197 | 2 |
| C2×AΣL(1,𝔽16) | 197 |