Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #27160848 | C2 | semidirect |
| 4. #27160838 | C2 | semidirect |
| 5. #544×C197 | C2 | semidirect |
| 21. C2×D788 | Q8 | semidirect |
| 81. C197 | #2027 | semidirect |
| 83. #544 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161083 | 2 |
| #27160980 | 2 |
| #27160848 | 2 |
| #27160838 | 2 |
| #544×C197 | 2 |
| #2027 | 197 |