Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
222 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 222 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 |
| 4. #27160837 | C2 | semidirect |
| 5. #430×C197 | C2 | semidirect |
| 65. C197 | #2091 | semidirect |
| 68. #430 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161127 | 2 |
| #27161042 | 2 |
| #27160837 | 2 |
| #430×C197 | 2 |
| #2091 | 197 |