Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20263285 | C2 | semidirect |
| 3. #27161404 | C2 | semidirect |
| 4. #27161398 | C2 | semidirect |
| 5. #27161393 | C2 | semidirect |
| 6. #27161121 | C2 | semidirect |
| 7. #27161085 | C2 | semidirect |
| 8. #407×C197 | C2 | semidirect |
| 18. #20263285 | C22 | semidirect |
| 20. C2×C4⋊Dic197 | C22 | semidirect |
| 21. C2×C4⋊Dic197 | C22 | semidirect |
| 25. #20263260 | C22 | semidirect |
| 26. #20263258 | C22 | semidirect |
| 27. #20263248 | C22 | semidirect |
| 28. #20263248 | C22 | semidirect |
| 31. C22⋊C8×C197 | C22 | semidirect |
| 32. C22⋊C8×C197 | C22 | semidirect |
| 125. C197 | #3094 | semidirect |
| 134. #407 | D197 | semidirect |
| 157. C22⋊C8 | C2×D197 | semidirect |
| 158. C22⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263300 | 2 |
| C2×#20263285 | 2 |
| #27161404 | 2 |
| #27161398 | 2 |
| #27161393 | 2 |
| #27161121 | 2 |
| #27161085 | 2 |
| #407×C197 | 2 |
| #3094 | 197 |