Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27161556 | C2 | semidirect |
| 5. C2×#20263244 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. H(3,ℤ/4)×C197 | C2 | semidirect |
| 11. #20263326 | C4 | semidirect |
| 12. #20263314 | C4 | semidirect |
| 109. C197 | #1912 | semidirect |
| 117. H(3,ℤ/4) | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161655 | 2 |
| #27161556 | 2 |
| #27161097 | 2 |
| #27161095 | 2 |
| C2×#20263244 | 2 |
| #27160835 | 2 |
| H(3,ℤ/4)×C197 | 2 |
| #1912 | 197 |