Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161808 | C2 | semidirect |
| 4. #27161429 | C2 | semidirect |
| 5. #27161388 | C2 | semidirect |
| 8. #27161203 | C2 | semidirect |
| 9. Q16×Dic197 | C2 | semidirect |
| 11. #462×C197 | C2 | semidirect |
| 115. C197 | #3364 | semidirect |
| 124. #462 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161808 | 2 |
| #27161803 | 2 |
| #27161435 | 2 |
| #27161429 | 2 |
| #27161388 | 2 |
| #27161360 | 2 |
| #27161303 | 2 |
| #27161203 | 2 |
| Q16×Dic197 | 2 |
| C4×#15691345 | 2 |
| #462×C197 | 2 |
| #3364 | 197 |