Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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 |
|---|---|---|
| 1. C2×#20263374 | C2 | semidirect |
| 2. C2×#20263352 | C2 | semidirect |
| 3. #27161251 | C2 | direct (N × H) |
| 4. C2×#20263254 | C2 | semidirect |
| 5. C2×#20263245 | C2 | semidirect |
| 6. C2×#124×C197 | C2 | semidirect |
| 9. #20263374 | C22 | semidirect |
| 15. #20263352 | C22 | semidirect |
| 19. #20263254 | C22 | semidirect |
| 20. #20263245 | C22 | semidirect |
| 24. #124×C197 | C22 | semidirect |
| 114. C2×C197 | #454 | semidirect |
| 117. C197 | C2×#454 | semidirect |
| 121. C2×#124 | D197 | semidirect |
| 140. #124 | C2×D197 | semidirect |
| 233. C2 | #27161251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263374 | 2 |
| C2×#20263352 | 2 |
| #27161251 | 2 |
| C2×#20263254 | 2 |
| C2×#20263245 | 2 |
| C2×#124×C197 | 2 |
| C2×#454 | 197 |