Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161449 | C2 | semidirect |
| 3. #27161445 | C2 | semidirect |
| 4. #27161441 | C2 | semidirect |
| 5. #27161073 | C2 | semidirect |
| 6. C2×#20263237 | C2 | semidirect |
| 7. #533×C197 | C2 | semidirect |
| 78. C197 | #3135 | semidirect |
| 80. #533 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161629 | 2 |
| #27161449 | 2 |
| #27161445 | 2 |
| #27161441 | 2 |
| #27161073 | 2 |
| C2×#20263237 | 2 |
| #533×C197 | 2 |
| #3135 | 197 |