Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27161128 | C2 | semidirect |
| 3. #27161127 | C2 | semidirect |
| 6. #27160844 | C2 | semidirect |
| 7. #341×C197 | C2 | semidirect |
| 91. C197 | #1858 | semidirect |
| 99. #341 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161845 | 2 |
| #27161128 | 2 |
| #27161127 | 2 |
| #27161061 | 2 |
| #27161045 | 2 |
| #27160844 | 2 |
| #341×C197 | 2 |
| #1858 | 197 |