Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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. #27161833 | C2 | semidirect |
| 3. #27161445 | C2 | semidirect |
| 4. #27161444 | C2 | semidirect |
| 5. #27160820 | C2 | semidirect |
| 6. #27160818 | C2 | semidirect |
| 7. #330×C197 | C2 | semidirect |
| 97. C197 | #1657 | semidirect |
| 104. #330 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161833 | 2 |
| #27161468 | 2 |
| #27161445 | 2 |
| #27161444 | 2 |
| #27160820 | 2 |
| #27160818 | 2 |
| #330×C197 | 2 |
| #1657 | 197 |