Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161802 | C2 | semidirect |
| 3. #27161484 | C2 | semidirect |
| 4. #27161413 | C2 | semidirect |
| 5. #27161401 | C2 | semidirect |
| 6. #27161364 | C2 | semidirect |
| 7. #27161359 | C2 | semidirect |
| 8. #27161322 | C2 | semidirect |
| 9. #27161158 | C2 | semidirect |
| 10. #27161118 | C2 | semidirect |
| 11. C4×SD16×C197 | C2 | semidirect |
| 99. C8×C197 | #41 | semidirect |
| 122. C197 | #3353 | semidirect |
| 132. C4×SD16 | D197 | semidirect |
| 222. C8 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161802 | 2 |
| #27161734 | 2 |
| #27161484 | 2 |
| #27161413 | 2 |
| #27161401 | 2 |
| #27161364 | 2 |
| #27161359 | 2 |
| #27161322 | 2 |
| #27161158 | 2 |
| #27161118 | 2 |
| C4×SD16×C197 | 2 |
| #3353 | 197 |