Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #27161553 | C2 | semidirect |
| 3. #27161190 | C2 | semidirect |
| 4. #27161161 | C2 | semidirect |
| 5. #27161083 | C2 | semidirect |
| 6. #27161034 | C2 | semidirect |
| 7. #427×C197 | C2 | semidirect |
| 9. C2×D1576 | C4 | semidirect |
| 14. #20263288 | C22 | semidirect |
| 17. #20263246 | C22 | semidirect |
| 18. #20263236 | C22 | semidirect |
| 19. C8×Dic197 | C22 | semidirect |
| 22. #107×C197 | C22 | semidirect |
| 23. #106×C197 | C22 | semidirect |
| 27. C2×D788 | C2×C4 | semidirect |
| 30. D1576 | C2×C4 | semidirect |
| 31. D1576 | C2×C4 | semidirect |
| 39. C2×C8×C197 | C2×C4 | semidirect |
| 77. C197 | #2948 | semidirect |
| 83. #427 | D197 | semidirect |
| 97. #107 | C2×D197 | semidirect |
| 98. #106 | C2×D197 | semidirect |
| 113. C2×C8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1576 | 2 |
| #27161553 | 2 |
| #27161190 | 2 |
| #27161161 | 2 |
| #27161083 | 2 |
| #27161034 | 2 |
| #427×C197 | 2 |
| #2948 | 197 |