Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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. #27161476 | C2 | semidirect |
| 3. #27160903 | C2 | semidirect |
| 4. #27160899 | C2 | semidirect |
| 7. #365×C197 | C2 | semidirect |
| 21. Dic788 | Q8 | semidirect |
| 23. D1576 | Q8 | semidirect |
| 60. C197 | #2230 | semidirect |
| 65. #365 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161476 | 2 |
| #27161195 | 2 |
| #27160903 | 2 |
| #27160899 | 2 |
| #27160890 | 2 |
| #27160888 | 2 |
| #365×C197 | 2 |
| #2230 | 197 |