Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27161136 | C2 | semidirect |
| 3. #27160804 | C2 | semidirect |
| 5. #431×C197 | C2 | semidirect |
| 92. C197 | #1473 | semidirect |
| 96. #431 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263320 | 2 |
| #27161136 | 2 |
| #27160804 | 2 |
| #27160802 | 2 |
| #431×C197 | 2 |
| #1473 | 197 |