Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 2. #27161445 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161376 | C2 | semidirect |
| 5. #27161356 | C2 | semidirect |
| 6. #27161279 | C2 | semidirect |
| 7. #27161279 | C2 | semidirect |
| 8. #27161210 | C2 | semidirect |
| 9. #27161177 | C2 | semidirect |
| 10. C4×#15691345 | C2 | semidirect |
| 11. #557×C197 | C2 | semidirect |
| 93. Q8×C197 | #41 | semidirect |
| 124. C197 | #3368 | semidirect |
| 126. #557 | D197 | semidirect |
| 204. Q8 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161751 | 2 |
| #27161445 | 2 |
| #27161427 | 2 |
| #27161376 | 2 |
| #27161356 | 2 |
| #27161279 | 2 |
| #27161210 | 2 |
| #27161177 | 2 |
| C4×#15691345 | 2 |
| #557×C197 | 2 |
| #3368 | 197 |