Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27160982 | C2 | semidirect |
| 3. #27160979 | C2 | semidirect |
| 4. #27160973 | C2 | semidirect |
| 5. #27160971 | C2 | semidirect |
| 6. #27160968 | C2 | semidirect |
| 7. #27160958 | C2 | semidirect |
| 8. #27160934 | C2 | semidirect |
| 9. #386×C197 | C2 | semidirect |
| 12. #20263294 | C4 | semidirect |
| 13. C2×C4⋊Dic197 | C22 | semidirect |
| 14. C2×#15691337 | C22 | semidirect |
| 17. C2×C22⋊Dic197 | C22 | semidirect |
| 23. C2×C4×Dic197 | C22 | semidirect |
| 24. C2×C4×Dic197 | C22 | semidirect |
| 25. #20263233 | C22 | semidirect |
| 26. #20263233 | C22 | semidirect |
| 28. C23×C4×C197 | C22 | semidirect |
| 30. C2×C22⋊C4×C197 | C22 | semidirect |
| 31. #95×C197 | C22 | semidirect |
| 36. C23×D197 | C2×C4 | semidirect |
| 48. C22⋊Dic197 | C2×C4 | semidirect |
| 53. #15691335 | C2×C4 | semidirect |
| 149. C197 | #2375 | semidirect |
| 158. #386 | D197 | semidirect |
| 163. C23×C4 | C2×D197 | semidirect |
| 176. C2×C22⋊C4 | C2×D197 | semidirect |
| 181. #95 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263294 | 2 |
| #27160982 | 2 |
| #27160979 | 2 |
| #27160973 | 2 |
| #27160971 | 2 |
| #27160968 | 2 |
| #27160958 | 2 |
| #27160934 | 2 |
| #386×C197 | 2 |
| #2375 | 197 |