Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
206 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #27161519 | C2 | semidirect |
| 2. C2×#20263272 | C2 | semidirect |
| 3. #27161354 | C2 | semidirect |
| 4. #27160895 | C2 | semidirect |
| 5. #27160886 | C2 | semidirect |
| 6. #27160863 | C2 | semidirect |
| 88. C197 | #2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161519 | 2 |
| C2×#20263272 | 2 |
| #27161354 | 2 |
| #27160895 | 2 |
| #27160886 | 2 |
| #27160863 | 2 |
| #578×C197 | 2 |
| #2195 | 197 |