Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C22⋊#13096802 | C2 | semidirect |
| 3. #27160815 | C2 | semidirect |
| 4. #27160812 | C2 | semidirect |
| 5. C4×C22⋊C4×C197 | C2 | semidirect |
| 6. C2×#15691358 | C4 | semidirect |
| 9. #20263305 | C4 | semidirect |
| 11. #20263300 | C4 | semidirect |
| 16. #20263285 | C4 | semidirect |
| 112. C197 | #1501 | semidirect |
| 116. C4×C22⋊C4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161590 | 2 |
| C2×C22⋊#13096802 | 2 |
| #27160815 | 2 |
| #27160812 | 2 |
| C4×C22⋊C4×C197 | 2 |
| #1501 | 197 |