Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27161705 | C2 | semidirect |
| 3. #27160846 | C2 | semidirect |
| 4. #27160845 | C2 | semidirect |
| 30. C24×C197 | Q8 | semidirect |
| 93. C197 | #2029 | semidirect |
| 114. C24 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161705 | 2 |
| #27160935 | 2 |
| #27160846 | 2 |
| #27160845 | 2 |
| #379×C197 | 2 |
| #2029 | 197 |