Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161376 | C2 | semidirect |
| 3. #27161376 | C2 | semidirect |
| 4. #27161366 | C2 | semidirect |
| 5. #27161356 | C2 | semidirect |
| 6. #27161119 | C2 | semidirect |
| 7. #27161115 | C2 | semidirect |
| 8. #27161106 | C2 | semidirect |
| 11. #544×C197 | C2 | semidirect |
| 21. #20263259 | C22 | semidirect |
| 22. #20263259 | C22 | semidirect |
| 23. #20263259 | C22 | semidirect |
| 24. #20263257 | C22 | semidirect |
| 25. #20263257 | C22 | semidirect |
| 26. #20263257 | C22 | semidirect |
| 27. C4⋊#13096802 | C22 | semidirect |
| 28. C4⋊#13096802 | C22 | semidirect |
| 34. C4⋊Q8×C197 | C22 | semidirect |
| 36. #125×C197 | C22 | semidirect |
| 44. C2×D788 | Q8 | semidirect |
| 124. C197 | #3081 | semidirect |
| 126. #544 | D197 | semidirect |
| 141. C4⋊Q8 | C2×D197 | semidirect |
| 143. #125 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161553 | 2 |
| #27161376 | 2 |
| #27161366 | 2 |
| #27161356 | 2 |
| #27161119 | 2 |
| #27161115 | 2 |
| #27161106 | 2 |
| #27161083 | 2 |
| C2×#20263246 | 2 |
| #544×C197 | 2 |
| #3081 | 197 |