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. #27161615 | C2 | semidirect |
| 2. #27161480 | C2 | semidirect |
| 3. #27161464 | C2 | semidirect |
| 4. #27161435 | C2 | semidirect |
| 6. #27161310 | C2 | semidirect |
| 7. Q16×Dic197 | C2 | semidirect |
| 8. #27161164 | C2 | semidirect |
| 9. #27161161 | C2 | semidirect |
| 10. C2×C8×Dic197 | C2 | semidirect |
| 11. #467×C197 | C2 | semidirect |
| 118. C197 | #3168 | semidirect |
| 124. #467 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161615 | 2 |
| #27161480 | 2 |
| #27161464 | 2 |
| #27161435 | 2 |
| #27161315 | 2 |
| #27161310 | 2 |
| Q16×Dic197 | 2 |
| #27161164 | 2 |
| #27161161 | 2 |
| C2×C8×Dic197 | 2 |
| #467×C197 | 2 |
| #3168 | 197 |