Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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. #27160940 | C2 | semidirect |
| 4. #27160936 | C2 | semidirect |
| 6. C4×#15691335 | C2 | semidirect |
| 7. C2×#117×C197 | C2 | semidirect |
| 12. C22×C4×D197 | C4 | semidirect |
| 16. C2×C4⋊Dic197 | C22 | semidirect |
| 19. C2×C4×Dic197 | C22 | semidirect |
| 20. #20263233 | C22 | semidirect |
| 23. C2×C4⋊C4×C197 | C22 | semidirect |
| 25. C2×C42×C197 | C22 | semidirect |
| 81. C2×C4×C197 | C22⋊C4 | semidirect |
| 101. C2×D197 | #117 | semidirect |
| 113. C197 | #2280 | semidirect |
| 117. C2×#117 | D197 | semidirect |
| 133. C2×C4⋊C4 | C2×D197 | semidirect |
| 138. C2×C42 | C2×D197 | semidirect |
| 195. C2×C4 | #15691335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D197 | 2 |
| C2×#20263285 | 2 |
| #27160940 | 2 |
| #27160936 | 2 |
| #27160934 | 2 |
| C4×#15691335 | 2 |
| C2×#117×C197 | 2 |
| #2280 | 197 |