Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#20263261 | C2 | semidirect |
| 4. C2×#20263245 | C2 | semidirect |
| 6. #27161035 | C2 | semidirect |
| 7. #419×C197 | C2 | semidirect |
| 12. C2×#15691345 | C4 | semidirect |
| 106. C197 | #1977 | semidirect |
| 110. #419 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691345 | 2 |
| C2×#20263261 | 2 |
| #27161083 | 2 |
| C2×#20263245 | 2 |
| C2×#20263242 | 2 |
| #27161035 | 2 |
| #419×C197 | 2 |
| #1977 | 197 |