Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #27161115 | C2 | direct (N × H) |
| 4. C2×#20263259 | C2 | semidirect |
| 5. C2×#20263257 | C2 | semidirect |
| 7. C22×#13096802 | C4 | semidirect |
| 16. #20263259 | C22 | semidirect |
| 17. #20263257 | C22 | semidirect |
| 27. C2×#13096802 | C2×C4 | semidirect |
| 78. C2×C197 | #427 | semidirect |
| 81. C197 | C2×#427 | semidirect |
| 160. C2 | #27161115 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13096802 | 2 |
| C2×#20263285 | 2 |
| #27161115 | 2 |
| C2×#20263259 | 2 |
| C2×#20263257 | 2 |
| C2×#117×C197 | 2 |
| C2×#427 | 197 |