Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27161610 | C2 | semidirect |
| 2. #27161480 | C2 | semidirect |
| 3. #27161462 | C2 | semidirect |
| 4. #27161432 | C2 | semidirect |
| 5. #27161320 | C2 | semidirect |
| 6. #27161306 | C2 | semidirect |
| 7. #27161173 | C2 | semidirect |
| 8. #27161170 | C2 | semidirect |
| 9. D8×Dic197 | C2 | semidirect |
| 10. C2×C8×Dic197 | C2 | semidirect |
| 118. C197 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161610 | 2 |
| #27161480 | 2 |
| #27161462 | 2 |
| #27161432 | 2 |
| #27161320 | 2 |
| #27161306 | 2 |
| #27161173 | 2 |
| #27161170 | 2 |
| D8×Dic197 | 2 |
| C2×C8×Dic197 | 2 |
| #466×C197 | 2 |
| #3168 | 197 |