Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27161127 | C2 | semidirect |
| 2. #27161105 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. #424×C197 | C2 | semidirect |
| 89. C197 | #2098 | semidirect |
| 93. #424 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161127 | 2 |
| #27161105 | 2 |
| #27161097 | 2 |
| #27161095 | 2 |
| #27161045 | 2 |
| #27160835 | 2 |
| #424×C197 | 2 |
| #2098 | 197 |