Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #27161846 | C2 | semidirect |
| 3. #27161097 | C2 | semidirect |
| 4. #27161045 | C2 | semidirect |
| 5. #27160849 | C2 | semidirect |
| 6. #27160844 | C2 | semidirect |
| 7. #416×C197 | C2 | semidirect |
| 10. #20263356 | C4 | semidirect |
| 12. #20263351 | C4 | semidirect |
| 118. C197 | #1881 | semidirect |
| 123. #416 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| #27161846 | 2 |
| #27161097 | 2 |
| #27161045 | 2 |
| #27160849 | 2 |
| #27160844 | 2 |
| #416×C197 | 2 |
| #1881 | 197 |