Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
158 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 48 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. #27165816 | C2 | semidirect |
| 2. #27165796 | C2 | semidirect |
| 3. #27165795 | C2 | semidirect |
| 10. C2×Dic802 | C4 | semidirect |
| 12. C2×C22⋊D401 | C4 | semidirect |
| 14. C2×C4×D401 | C4 | semidirect |
| 16. C22×C4×C401 | C4 | semidirect |
| 53. C401 | #410 | semidirect |
| 67. C22×C4 | #13107944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27165816 | 2 |
| #27165796 | 2 |
| #27165795 | 2 |
| C2×#20264366 | 2 |
| #410 | 401 |