Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27161417 | C2 | semidirect |
| 3. #27161376 | C2 | semidirect |
| 4. #27161281 | C2 | semidirect |
| 6. #27161177 | C2 | semidirect |
| 7. C4×#15691345 | C2 | semidirect |
| 8. #27161140 | C2 | semidirect |
| 9. #541×C197 | C2 | semidirect |
| 18. #20263259 | C22 | semidirect |
| 19. #20263257 | C22 | semidirect |
| 20. C4⋊#13096802 | C22 | semidirect |
| 21. #20263250 | C22 | semidirect |
| 22. #20263250 | C22 | semidirect |
| 26. #20263237 | C22 | semidirect |
| 27. C4×#13096802 | C22 | semidirect |
| 28. C4⋊Q8×C197 | C22 | semidirect |
| 31. #125×C197 | C22 | semidirect |
| 33. C4×Q8×C197 | C22 | semidirect |
| 102. C197 | #3123 | semidirect |
| 104. #541 | D197 | semidirect |
| 116. C4⋊Q8 | C2×D197 | semidirect |
| 119. #125 | C2×D197 | semidirect |
| 121. C4×Q8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161553 | 2 |
| #27161417 | 2 |
| #27161376 | 2 |
| #27161281 | 2 |
| #27161229 | 2 |
| #27161177 | 2 |
| C4×#15691345 | 2 |
| #27161140 | 2 |
| #541×C197 | 2 |
| #3123 | 197 |