Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D788 | C2 | semidirect |
| 2. #27161438 | C2 | semidirect |
| 3. #27161429 | C2 | semidirect |
| 4. #27161374 | C2 | semidirect |
| 5. #27161359 | C2 | semidirect |
| 7. #27161281 | C2 | semidirect |
| 8. #27161210 | C2 | semidirect |
| 9. #27161177 | C2 | semidirect |
| 11. #556×C197 | C2 | semidirect |
| 122. C197 | #3367 | semidirect |
| 124. #556 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D788 | 2 |
| #27161438 | 2 |
| #27161429 | 2 |
| #27161374 | 2 |
| #27161359 | 2 |
| #27161291 | 2 |
| #27161281 | 2 |
| #27161210 | 2 |
| #27161177 | 2 |
| C4×#15691343 | 2 |
| #556×C197 | 2 |
| #3367 | 197 |