Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×Q8×Dic197 | C2 | semidirect |
| 3. #27161393 | C2 | semidirect |
| 4. #27161390 | C2 | semidirect |
| 5. #27161372 | C2 | semidirect |
| 6. #27161277 | C2 | semidirect |
| 7. #27161218 | C2 | semidirect |
| 8. #27161182 | C2 | semidirect |
| 9. #27161180 | C2 | semidirect |
| 10. #27161133 | C2 | semidirect |
| 11. #448×C197 | C2 | semidirect |
| 104. Q8×C197 | #41 | semidirect |
| 140. C197 | #3112 | semidirect |
| 149. #448 | D197 | semidirect |
| 229. Q8 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161624 | 2 |
| C2×Q8×Dic197 | 2 |
| #27161393 | 2 |
| #27161390 | 2 |
| #27161372 | 2 |
| #27161277 | 2 |
| #27161218 | 2 |
| #27161182 | 2 |
| #27161180 | 2 |
| #27161133 | 2 |
| #448×C197 | 2 |
| #3112 | 197 |