Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20263346 | C2 | semidirect |
| 2. #27161629 | C2 | semidirect |
| 3. #27161474 | C2 | semidirect |
| 4. #27161471 | C2 | semidirect |
| 5. #27161469 | C2 | semidirect |
| 6. #27161466 | C2 | semidirect |
| 7. C2×#20263237 | C2 | semidirect |
| 8. #532×C197 | C2 | semidirect |
| 40. C2×#13096802 | D4 | semidirect |
| 97. C197 | #3150 | semidirect |
| 101. #532 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| #27161629 | 2 |
| #27161474 | 2 |
| #27161471 | 2 |
| #27161469 | 2 |
| #27161466 | 2 |
| C2×#20263237 | 2 |
| #532×C197 | 2 |
| #3150 | 197 |