Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #27161636 | C2 | semidirect |
| 3. #27161477 | C2 | semidirect |
| 4. #27161452 | C2 | semidirect |
| 5. #27161430 | C2 | semidirect |
| 6. #27161426 | C2 | semidirect |
| 7. #27161308 | C2 | semidirect |
| 8. C4×#15691347 | C2 | semidirect |
| 9. C2×C4×C8×C197 | C2 | semidirect |
| 82. C2×C4×C197 | SD16 | semidirect |
| 90. C8×C197 | #41 | semidirect |
| 112. C197 | #3167 | semidirect |
| 122. C2×C4×C8 | D197 | semidirect |
| 195. C2×C4 | #15691347 | semidirect |
| 203. C8 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| #27161629 | 2 |
| #27161477 | 2 |
| #27161452 | 2 |
| #27161430 | 2 |
| #27161426 | 2 |
| #27161308 | 2 |
| C4×#15691347 | 2 |
| C2×C4×C8×C197 | 2 |
| #3167 | 197 |