Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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×#20263332 | C2 | semidirect |
| 3. #27161202 | C2 | semidirect |
| 4. #27161197 | C2 | semidirect |
| 5. #27161128 | C2 | semidirect |
| 6. #27161097 | C2 | semidirect |
| 7. #405×C197 | C2 | semidirect |
| 9. #20263359 | C4 | semidirect |
| 10. #20263354 | C4 | semidirect |
| 14. #20263332 | C22 | semidirect |
| 15. #20263332 | C22 | semidirect |
| 19. #20263262 | C22 | semidirect |
| 20. #20263254 | C22 | semidirect |
| 24. #97×C197 | C22 | semidirect |
| 25. C4×C8×C197 | C22 | semidirect |
| 89. C197 | #2955 | semidirect |
| 97. #405 | D197 | semidirect |
| 114. #97 | C2×D197 | semidirect |
| 115. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161879 | 2 |
| C2×#20263332 | 2 |
| #27161202 | 2 |
| #27161197 | 2 |
| #27161128 | 2 |
| #27161097 | 2 |
| #405×C197 | 2 |
| #2955 | 197 |