Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #27161846 | C2 | semidirect |
| 3. #27161097 | C2 | semidirect |
| 4. C2×#20263254 | C2 | semidirect |
| 5. C4×#41×C197 | C2 | semidirect |
| 7. #20263373 | C4 | semidirect |
| 8. #20263372 | C4 | semidirect |
| 13. C2×#15691342 | C22 | semidirect |
| 14. #20263254 | C22 | semidirect |
| 15. #20263254 | C22 | semidirect |
| 19. #117×C197 | C22 | semidirect |
| 20. C2×C42×C197 | C22 | semidirect |
| 24. #15691358 | C2×C4 | semidirect |
| 27. C2×Dic394 | C2×C4 | semidirect |
| 29. C2×D788 | C2×C4 | semidirect |
| 83. C197 | #2901 | semidirect |
| 87. C4×#41 | D197 | semidirect |
| 101. #117 | C2×D197 | semidirect |
| 102. C2×C42 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161915 | 2 |
| #27161846 | 2 |
| #27161097 | 2 |
| C2×#20263254 | 2 |
| C4×#41×C197 | 2 |
| #2901 | 197 |