Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
130 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 22. Dic788 | Q8 | semidirect |
| 59. C197 | #2225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161483 | 2 |
| #27161173 | 2 |
| #27160906 | 2 |
| #27160897 | 2 |
| #27160884 | 2 |
| #27160882 | 2 |
| #367×C197 | 2 |
| #2225 | 197 |