Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161807 | C2 | semidirect |
| 4. #27161430 | C2 | semidirect |
| 5. #27161387 | C2 | semidirect |
| 8. #27161290 | C2 | semidirect |
| 9. C4×Dic788 | C2 | semidirect |
| 11. C8×Q8×C197 | C2 | semidirect |
| 115. C197 | #3364 | semidirect |
| 125. C8×Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161807 | 2 |
| #27161802 | 2 |
| #27161434 | 2 |
| #27161430 | 2 |
| #27161387 | 2 |
| #27161360 | 2 |
| #27161302 | 2 |
| #27161290 | 2 |
| C4×Dic788 | 2 |
| C4×#15691347 | 2 |
| C8×Q8×C197 | 2 |
| #3364 | 197 |