Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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. #27160970 | C2 | semidirect |
| 3. #27160968 | C2 | semidirect |
| 4. #27160937 | C2 | semidirect |
| 6. C4×C22⋊Dic197 | C2 | semidirect |
| 7. C4×C22⋊C4×C197 | C2 | semidirect |
| 10. C2×#15691337 | C22 | semidirect |
| 12. C2×#15691335 | C4 | semidirect |
| 17. C2×C4×Dic197 | C22 | semidirect |
| 18. #20263233 | C22 | semidirect |
| 19. #20263233 | C22 | semidirect |
| 22. C2×C42×C197 | C22 | semidirect |
| 23. #95×C197 | C22 | semidirect |
| 99. C197 | #2312 | semidirect |
| 107. C4×C22⋊C4 | D197 | semidirect |
| 120. C2×C42 | C2×D197 | semidirect |
| 123. #95 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691335 | 2 |
| #27160970 | 2 |
| #27160968 | 2 |
| #27160937 | 2 |
| #27160934 | 2 |
| C4×C22⋊Dic197 | 2 |
| C4×C22⋊C4×C197 | 2 |
| #2312 | 197 |