Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#15691348 | C2 | semidirect |
| 2. C22×#15691346 | C2 | semidirect |
| 3. C2×#20263305 | C2 | semidirect |
| 4. #27161241 | C2 | direct (N × H) |
| 5. C2×#20263250 | C2 | semidirect |
| 6. C2×#20263247 | C2 | semidirect |
| 7. C2×C22⋊#13096802 | C2 | semidirect |
| 11. C2×#15691348 | C22 | semidirect |
| 13. C2×#15691346 | C22 | semidirect |
| 17. #20263305 | C22 | semidirect |
| 21. #20263250 | C22 | semidirect |
| 22. #20263247 | C22 | semidirect |
| 23. C22⋊#13096802 | C22 | semidirect |
| 131. C2×C197 | #452 | semidirect |
| 135. C197 | C2×#452 | semidirect |
| 267. C2 | #27161241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691348 | 2 |
| C22×#15691346 | 2 |
| C2×#20263305 | 2 |
| #27161241 | 2 |
| C2×#20263250 | 2 |
| C2×#20263247 | 2 |
| C2×C22⋊#13096802 | 2 |
| C22×#41×C197 | 2 |
| C2×#452 | 197 |