Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 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. #27161102 | C2 | semidirect |
| 3. C2×#20263244 | C2 | semidirect |
| 4. C2×#20263244 | C2 | semidirect |
| 6. M16×Dic197 | C2 | semidirect |
| 108. C197 | #1967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263313 | 2 |
| #27161102 | 2 |
| C2×#20263244 | 2 |
| C2×#20263243 | 2 |
| M16×Dic197 | 2 |
| C2×#100×C197 | 2 |
| #1967 | 197 |