Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #27161423 | C2 | semidirect |
| 4. #27161422 | C2 | semidirect |
| 5. #27161416 | C2 | semidirect |
| 6. #27161411 | C2 | semidirect |
| 7. #27161115 | C2 | semidirect |
| 8. #27161089 | C2 | semidirect |
| 9. C2×#20263249 | C2 | semidirect |
| 11. #428×C197 | C2 | semidirect |
| 126. C197 | #3097 | semidirect |
| 134. #428 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161655 | 2 |
| #27161560 | 2 |
| #27161423 | 2 |
| #27161422 | 2 |
| #27161416 | 2 |
| #27161411 | 2 |
| #27161115 | 2 |
| #27161089 | 2 |
| C2×#20263249 | 2 |
| #27161047 | 2 |
| #428×C197 | 2 |
| #3097 | 197 |