Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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×#20263333 | C2 | semidirect |
| 3. #27161083 | C2 | semidirect |
| 4. #27161078 | C2 | semidirect |
| 5. #27161073 | C2 | semidirect |
| 6. C2×#20263246 | C2 | semidirect |
| 7. #520×C197 | C2 | semidirect |
| 9. #20263372 | C4 | semidirect |
| 15. C2×#15691342 | C22 | semidirect |
| 16. C22×#13096802 | C22 | semidirect |
| 17. #20263249 | C22 | semidirect |
| 18. #20263249 | C22 | semidirect |
| 19. #20263246 | C22 | semidirect |
| 20. #20263246 | C22 | semidirect |
| 21. #20263246 | C22 | semidirect |
| 25. #117×C197 | C22 | semidirect |
| 26. C2×C4⋊C4×C197 | C22 | semidirect |
| 30. #15691358 | C2×C4 | semidirect |
| 34. C2×D788 | C2×C4 | semidirect |
| 97. C197 | #2897 | semidirect |
| 101. #520 | D197 | semidirect |
| 118. #117 | C2×D197 | semidirect |
| 119. C2×C4⋊C4 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263372 | 2 |
| C2×#20263333 | 2 |
| #27161083 | 2 |
| #27161078 | 2 |
| #27161073 | 2 |
| C2×#20263246 | 2 |
| #520×C197 | 2 |
| #2897 | 197 |