Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #27161177 | C2 | semidirect |
| 4. C4×#15691345 | C2 | semidirect |
| 5. #27161115 | C2 | semidirect |
| 6. #27161088 | C2 | semidirect |
| 8. #27161035 | C2 | semidirect |
| 9. #519×C197 | C2 | semidirect |
| 11. C2×#15691345 | C4 | semidirect |
| 20. #20263259 | C22 | semidirect |
| 21. #20263257 | C22 | semidirect |
| 22. #20263250 | C22 | semidirect |
| 24. #20263237 | C22 | semidirect |
| 25. C4×#13096802 | C22 | semidirect |
| 28. C4×Q8×C197 | C22 | semidirect |
| 38. #15691345 | C2×C4 | semidirect |
| 39. #15691345 | C2×C4 | semidirect |
| 41. C2×#13096802 | C2×C4 | semidirect |
| 51. C2×Q8×C197 | C2×C4 | semidirect |
| 103. C197 | #2949 | semidirect |
| 106. #519 | D197 | semidirect |
| 122. C4×Q8 | C2×D197 | semidirect |
| 139. C2×Q8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691345 | 2 |
| #27161553 | 2 |
| #27161177 | 2 |
| C4×#15691345 | 2 |
| #27161115 | 2 |
| #27161088 | 2 |
| #27161083 | 2 |
| #27161035 | 2 |
| #519×C197 | 2 |
| #2949 | 197 |