Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4⋊C4×D197 | C2 | semidirect |
| 3. #27161399 | C2 | direct (N × H) |
| 4. C2×#20263257 | C2 | semidirect |
| 5. C2×#20263248 | C2 | semidirect |
| 6. C2×#20263246 | C2 | semidirect |
| 7. C2×#20263238 | C2 | semidirect |
| 8. C2×#106×C197 | C2 | semidirect |
| 19. C4⋊C4×D197 | C22 | semidirect |
| 21. #20263257 | C22 | semidirect |
| 22. #20263248 | C22 | semidirect |
| 23. #20263246 | C22 | semidirect |
| 24. #20263238 | C22 | semidirect |
| 28. #106×C197 | C22 | semidirect |
| 110. C2×C197 | #481 | semidirect |
| 116. C197 | C2×#481 | semidirect |
| 122. C2×#106 | D197 | semidirect |
| 142. #106 | C2×D197 | semidirect |
| 229. C2 | #27161399 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263301 | 2 |
| C2×C4⋊C4×D197 | 2 |
| #27161399 | 2 |
| C2×#20263257 | 2 |
| C2×#20263248 | 2 |
| C2×#20263246 | 2 |
| C2×#20263238 | 2 |
| C2×#106×C197 | 2 |
| C2×#481 | 197 |