Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161366 | C2 | semidirect |
| 4. #27161356 | C2 | semidirect |
| 5. #27161122 | C2 | semidirect |
| 6. #27161103 | C2 | semidirect |
| 8. #533×C197 | C2 | semidirect |
| 18. #20263259 | C22 | semidirect |
| 19. #20263257 | C22 | semidirect |
| 20. C4⋊#13096802 | C22 | semidirect |
| 21. C4⋊#13096802 | C22 | semidirect |
| 24. C4⋊Q8×C197 | C22 | semidirect |
| 25. C4⋊Q8×C197 | C22 | semidirect |
| 26. #125×C197 | C22 | semidirect |
| 36. C2×D788 | Q8 | semidirect |
| 115. C197 | #3077 | semidirect |
| 117. #533 | D197 | semidirect |
| 128. C4⋊Q8 | C2×D197 | semidirect |
| 129. C4⋊Q8 | C2×D197 | semidirect |
| 130. #125 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D788 | 2 |
| #27161376 | 2 |
| #27161366 | 2 |
| #27161356 | 2 |
| #27161122 | 2 |
| #27161103 | 2 |
| #27161083 | 2 |
| #533×C197 | 2 |
| #3077 | 197 |