Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161441 | C2 | semidirect |
| 3. #27161431 | C2 | semidirect |
| 4. #27161427 | C2 | semidirect |
| 5. #27161078 | C2 | semidirect |
| 6. C4×#15691342 | C2 | semidirect |
| 7. C2×C4⋊Q8×C197 | C2 | semidirect |
| 100. C197 | #3141 | semidirect |
| 103. C2×C4⋊Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161629 | 2 |
| #27161441 | 2 |
| #27161431 | 2 |
| #27161427 | 2 |
| #27161078 | 2 |
| C4×#15691342 | 2 |
| C2×C4⋊Q8×C197 | 2 |
| #3141 | 197 |