Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 1. #27161483 | C2 | semidirect |
| 3. #27160904 | C2 | semidirect |
| 4. #27160897 | C2 | semidirect |
| 7. #366×C197 | C2 | semidirect |
| 23. D1576 | Q8 | semidirect |
| 63. C197 | #2224 | semidirect |
| 68. #366 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161483 | 2 |
| #27161161 | 2 |
| #27160904 | 2 |
| #27160897 | 2 |
| #27160881 | 2 |
| #27160879 | 2 |
| #366×C197 | 2 |
| #2224 | 197 |