Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 31. C2×Dic394 | Q8 | semidirect |
| 104. C197 | #2028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161089 | 2 |
| #27161087 | 2 |
| #27160985 | 2 |
| #27160847 | 2 |
| #27160839 | 2 |
| #339×C197 | 2 |
| #2028 | 197 |